<div dir="ltr"><div><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline">Sayın Liste Üyeleri,</span><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline"> </span><br></div><div><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline"><br></span></div><div><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit">Gebze Teknik Üniversitesi (GTÜ) Matematik Bölümü Genel Seminerleri kapsamında, 30 Ekim Cuma günü saat 14:00'te<span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"> </span></span><span style="font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><b> Dr. Öğr. Üyesi Önder Türk </b><span style="font-weight:inherit"> (G</span></span><span style="font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><span style="font-style:inherit">TÜ)</span><span style="margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"><i>  </i></span></span><span style="margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><i style=""><font face="Times New Roman, Times, serif">“</font><font face="times new roman, serif"> </font></i><font face="times new roman, serif"><i><span style="color:rgb(0,0,0)">Modal Analysis of Incompressible Elastic Waves Based on a Stabilized Finite Element Method</span> </i></font></span><span style="font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><i>”  </i></span><span style="font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit">başlıklı bir seminer verecektir. Seminerin detayları aşağıda olup tüm ilgilenenler davetlidir. </span><span style="font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"> </span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Seminer için Microsoft Teams platformu kullanılacaktır. Seminere katılmak için aşağıdaki linki kullanabilirsiniz:</span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><a href="https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1603456597648?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d" target="_blank" rel="noopener noreferrer" id="gmail-LPlnk681967" style="margin:0px;padding:0px;border:0px;font-variant-numeric:inherit;font-variant-east-asian:inherit;font-stretch:inherit;font-size:16px;line-height:inherit;font-family:Calibri,Arial,Helvetica,sans-serif;vertical-align:baseline;outline:0px">https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1603456597648?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d</a>  <br></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><span style="color:black;font-family:"Times New Roman",Times,serif;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;font-weight:inherit">Seminere bağlanırken aşağıdaki pencereyi görürseniz,  </span><br></p><div><div style="margin:0px;padding:0px 0px 20px;width:1292.01px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:medium"><div><div id="gmail-m_7125744001494289074gmail-m_6627495338753105945gmail-:vu" style="font-size:0.875rem;direction:ltr;margin:8px 0px 0px;padding:0px"><div id="gmail-m_7125744001494289074gmail-m_6627495338753105945gmail-:vv" style="overflow:hidden;font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:small;line-height:1.5;font-family:Arial,Helvetica,sans-serif"><div dir="ltr"><p style="margin:0cm 0cm 0pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;font-size:11pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><br></p><div><img src="cid:ii_kfs6ydpf0" alt="image.png" width="327" height="165" class="gmail-CToWUd gmail-a6T" tabindex="0" style="cursor: pointer; outline: 0px;"><span style="color:black;font-family:"Times New Roman",Times,serif;font-size:12pt;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;font-weight:inherit;text-align:center"> </span><br></div><p align="center" style="margin:0cm 0cm 0pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;font-size:11pt;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;text-align:center"><br></p></div></div></div></div></div></div><p style="margin:0cm 0cm 0pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span lang="EN-US" style="font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black">lütfen</span><span lang="EN-US" style="font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black"><b><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"> </span>Allow (İzin ver) </b></span><span lang="EN-US" style="font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black">seçeneğine tıklayınız. Bu sizin toplantıya kamera ve mikrofonunuzla bağlanabilmenizi sağlar.</span><br></p><p style="margin:0cm 0cm 0pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",serif;vertical-align:baseline;color:black"><br></span></p><p style="margin:0cm 0cm 0pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black">Seminere giriş yaparken lütfen gerçek ve tam adınızı kullanınız.</span></p><p style="margin:0cm 0cm 0pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",serif;vertical-align:baseline;color:black"><br></span></p><p style="margin:0cm 0cm 0pt;color:rgb(32,31,30);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><font color="#000000" face="Times New Roman, serif"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Konuşmadığınız sürece lütfen mikrofonunuzu kapalı tutunuz.</span></font></p><br style="color:rgb(32,31,30)"><p style="margin-top:0px;margin-bottom:0px;color:rgb(32,31,30)"></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Saygılarımızla.</span><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit"> </span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><br></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Dear all,</span><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit"> </span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><span style="color:rgb(34,34,34)"><b>Dr. Öğr. Üyesi Önder Türk</b> </span><font face="times new roman, serif"><b> </b></font></span><span style="font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit">from Gebze Technical University will give a talk titled<span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"> </span></span><span style="font-family:"Times New Roman",Times,serif;margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><i>“</i></span><span style="font-family:"Times New Roman",Times,serif;color:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"><span style="margin:0px;padding:0px;border:0px;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;vertical-align:baseline;color:inherit"><i> Modal Analysis of Incompressible Elastic Waves Based on a Stabilized Finite Element Method</i><span style="font-style:inherit">  </span><i style="font-style:inherit">”</i></span><span style="font-style:inherit"> </span></span><span style="font-family:"Times New Roman",Times,serif;color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline">on 30th October, at 14:00.</span><span style="font-family:"Times New Roman",Times,serif;color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"> All interested are invited.</span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);line-height:22px"><font face="times new roman, serif"><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;vertical-align:baseline"><span style="color:rgb(0,0,0)">Abstract:</span> </span></font><span style="color:rgb(0,0,0);font-family:Calibri,Arial,Helvetica,sans-serif">Modal analysis is a typical approach employed to approximate vibration problems of elastic materials. The key idea is to assume a harmonic behaviour for the displacement utilizing the second order time derivatives in the inertia term, and thus to transform the problem into an eigenvalue problem. The set of equations is form identical to the Stokes equations which govern the incompressible creeping flow of viscous fluids, and is a constituent of Navier-Stokes equations. In this talk, will concentrate on a stabilized finite element  method formulated in a variational multiscale framework where the continuous space is approximated by a direct sum of the finite element space and its orthogonal complement. We shall show that the numerical procedure provides a reasonably realistic description of the eigenspectrum of the associated operator affirming that there are no spurious eigenvalues. Once the eigenspace has been built, the time approximation to the solution of the continuous problem is obtained making use of a few modes of the whole set, those with higher energy. The presentation will include several theoretical and numerical results from joint works with Daniele Boffi and Ramon Codina.</span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><span style="color:inherit;font-style:inherit;font-variant:inherit;font-weight:inherit;margin:0px;padding:0px;border:0px;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline"><br></span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Microsoft Teams platform will be used for the seminar. To join the seminar, please use the following link:</span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><a href="https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1603456597648?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d" target="_blank" rel="noopener noreferrer" id="gmail-LPlnk681967" style="margin:0px;padding:0px;border:0px;font-variant-numeric:inherit;font-variant-east-asian:inherit;font-stretch:inherit;font-size:16px;line-height:inherit;font-family:Calibri,Arial,Helvetica,sans-serif;vertical-align:baseline;outline:0px">https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1603456597648?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d</a>  <br></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black">If you see the following window when connecting to the seminar,  </span></span><br></p><div><img src="cid:ii_kfs6ydpv1" alt="image.png" width="327" height="165" class="gmail-CToWUd gmail-a6T" tabindex="0" style="cursor: pointer; outline: 0px;"><br></div><p align="center" style="margin:0cm 0cm 0pt;color:rgb(32,31,30);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;text-align:center;font-family:Calibri,sans-serif"><b><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"></span><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",serif;vertical-align:baseline;color:black"></span><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black"> </span></b></p><p style="margin:0cm 0cm 0pt;color:rgb(32,31,30);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-family:Calibri,sans-serif"><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black">please select</span><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:bold;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",serif;vertical-align:baseline;color:black"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit"> </span></span><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:bold;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black"><b>Allow</b></span><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black"><b>.<span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:inherit;vertical-align:baseline;color:inherit"> </span></b>Then you will be able to use your microphone and camera during the seminar. </span></p><p style="margin:0cm 0cm 0pt;color:rgb(32,31,30);background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-family:Calibri,sans-serif"><span lang="EN-US" style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:black"><br></span></p><p style="margin-top:0px;margin-bottom:0px;color:rgb(32,31,30)"></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:rgb(0,0,0)">Please use your real and complete name when you enter the system.</span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:normal;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Please switch your microphone off unless you are speaking.</span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit"><br></span></p><p style="margin:0cm 0cm 8pt;color:rgb(32,31,30);font-family:Calibri,sans-serif;line-height:22px"><span style="margin:0px;padding:0px;border:0px;font-style:inherit;font-variant:inherit;font-weight:inherit;font-stretch:inherit;line-height:inherit;font-family:"Times New Roman",Times,serif;vertical-align:baseline;color:inherit">Sincerely</span></p></div></div>