An edge‐based pressure stabilization technique for finite elements on arbitrarily anisotropic meshes

Frei Stefan

摘要

Summary > In this paper, we analyze a stabilized equal‐order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a subdomain, for example, along the boundary of the domain, with the only condition that a maximum angle is fulfilled in each element. This discretization is motivated by applications on moving domains as arising, for example, in fluid‐structure interaction or multiphase‐flow problems. To deal with the anisotropies, we define a modification of the original continuous interior penalty stabilization approach. We show analytically the discrete stability of the method and convergence of order <mat:math display="inline" altimg="urn:x-wiley:fld:media:fld4701:fld4701-math-0001" wiley:location="equation/fld4701-math-0001.png"> <mat:mi mathvariant="script">O</mat:mi> <mat:mo stretchy="false">(</mat:mo> <mat:msup> <mat:mi>h</mat:mi> <mat:mrow> <mat:mn>3</mat:mn> <mat:mo stretchy="false">/</mat:mo> <mat:mn>2</mat:mn> </mat:mrow> </mat:msup> <mat:mo stretchy="false">)</mat:mo> </mat:math> in the energy norm and <mat:math display="inline" altimg="urn:x-wiley:fld:media:fld4701:fld4701-math-0002" wiley:location="equation/fld4701-math-0002.png"> <mat:mi mathvariant="script">O</mat:mi> <mat:mo stretchy="false">(</mat:mo> <mat:msup> <mat:mi>h</mat:mi> <mat:mrow> <mat:mn>5</mat:mn> <mat:mo stretchy="false">/</mat:mo> <mat:mn>2</mat:mn> </mat:mrow> </mat:msup> <mat:mo stretchy="false">)</mat:mo> </mat:math> in the <fi>L</fi> 2 ‐norm of the velocities. We present numerical examples for a linear Stokes problem and for a nonlinear fluid‐structure interaction problem, which substantiate the analytical results and show the capabilities of the approach. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”XML：ID =“FLD4701-ABS-AB-0001”> <标题类型=“main”>摘要</ title> > 在本文中，我们分析了各向异性网格上的斯托克斯方程的稳定相等的有限元近似。特别地，我们允许子域中的任意各向异性，例如，沿域的边界，其中唯一的条件是在每个元件中满足最大角度的条件。这种离散化是通过在运动结构域的应用而产生的，例如，在流体结构相互作用或多相流动问题中。要处理各向同性，我们定义了原始持续内部惩罚稳定方法的修改。我们在分析上展示了方法的离散稳定性和订单融合 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：FLD：媒体：FLD4701：FLD4701-Math-0001”Wiley：Location =“等式/ FLD4701-Math-0001.png”> <mat：mi mathvariant =“脚本” </ mat：mi> <mat：mo stractry =“false”>（</ mat：mo> <mat：msup> <MAT：MI> H </ MAT：MI> <MAT：MROW> <MAT：MN> 3 </ MAT：MN> <MAT：MO弹力=“假”> / </ MAT：MO> <MAT：MN> 2 </ MAT：MN> </ mat：MROW> </ mat：msup> <mat：mo stractry =“假”>）</ mat：mo> </ mat：math> 在能量规范和 <mat：数学显示=“内联”Altimg =“URN：X-Wiley：FLD：媒体：FLD4701：FLD4701-Math-0002”Wiley：Location =“等式/ FLD4701-Math-0002.png”> <mat：mi mathvariant =“脚本” </ mat：mi> <mat：mo stractry =“false”>（</ mat：mo> <mat：msup> <MAT：MI> H </ MAT：MI> <MAT：MROW> <MAT：MN> 5 </ MAT：MN> <MAT：MO弹力=“假”> / </ MAT：MO> <MAT：MN> 2 </ MAT：MN> </ mat：MROW> </ mat：msup> <mat：mo stractry =“假”>）</ mat：mo> </ mat：math> 在里面 <fi> l </ fi> 2 </ sup> -norm的速度。我们为线性斯托克斯问题和非线性流体结构相互作用问题提供了数值示例，这证明了分析结果并显示了方法的能力。 </ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-20811/'>《International Journal for Numerical Methods in Fluids》</a> <b style="margin: 0 2px;">|</b><span>2019年第10期</span><b style="margin: 0 2px;">|</b><span>共23页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Frei Stefan&option=202" target="_blank" rel="nofollow">Frei Stefan;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department of MathematicsUniversity College LondonLondon UK;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/1155.html" title="流体力学">流体力学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=anisotropic meshes&option=203" rel="nofollow">anisotropic meshes;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=continuous interior penalty&option=203" rel="nofollow">continuous interior penalty;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=locally modified finite elements&option=203" rel="nofollow">locally modified finite elements;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=moving domains&option=203" rel="nofollow">moving domains;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=pressure stabilization&option=203" rel="nofollow">pressure stabilization;</a> </p> <div class="translation"> 机译：各向异性网状;连续内部惩罚;局部修改的有限元;移动域;压力稳定; </div> </li> </ul> </div> </div> <div class="literature cardcommon" id="literaturereference" style="display:none"> <div class="similarity "> <h3 class="all_title" id="enpatent111">引文网络</h3> <div class="referencetab clearfix"> <ul id="referencedaohang"> <li dataid="referenceul">参考文献</li> <li dataid="citationul">引证文献</li> <li dataid="commonreferenceul">共引文献</li> <li dataid="commoncitationul">同被引文献</li> <li dataid="tworeferenceul">二级参考文献</li> <li dataid="twocitationul">二级引证文献</li> </ul> </div> <div class="reference_details" id="referenceList"> <ul id="referenceul"></ul> <ul id="citationul"></ul> <ul id="commonreferenceul"></ul> <ul id="commoncitationul"></ul> <ul id="tworeferenceul"></ul> <ul id="twocitationul"></ul> </div> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704022975528.html">An edge‐based pressure stabilization technique for finite elements on arbitrarily anisotropic meshes</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Frei Stefan&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Frei Stefan </a> <a href="/journal-foreign-20811/" target="_blank" rel="nofollow" class="tuijian_authcolor">International Journal for Numerical Methods in Fluids .</a> <span>2019</span><span>,第10期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：基于边缘的压力稳定技术，用于在任意各向异性网眼上有限元</span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/070409012253.html">Stabilized finite elements on anisotropic meshes: A priori error estimates for the advection-diffusion and the Stokes problems</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Micheletti S.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Micheletti S.,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Perotto S.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Perotto S.,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Picasso M.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Picasso M. </a> <a href="/journal-foreign-28154/" target="_blank" rel="nofollow" class="tuijian_authcolor">SIAM Journal on Numerical Analysis .</a> <span>2003</span><span>,第3期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：各向异性网格上的稳定有限元：对流扩散和斯托克斯问题的先验误差估计</span> </p> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/070406425679.html">CONDITIONING OF FINITE ELEMENT EQUATIONS WITH ARBITRARY ANISOTROPIC MESHES</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=LENNARD KAMENSKI&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">LENNARD KAMENSKI,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=WEIZHANG HUANG&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">WEIZHANG HUANG,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=HONGGUO XU&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">HONGGUO XU </a> <a href="/journal-foreign-24551/" target="_blank" rel="nofollow" class="tuijian_authcolor">Mathematics of computation .</a> <span>2014</span><span>,第289期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：带有任意各向异性网格的有限元方程的条件</span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/academic-conference-foreign_meeting-199774_thesis/020513680996.html">Comparison of SU/PG and DG Finite-Element Techniques for the Compressible Navier-Stokes Equations on Anisotropic Unstructured Meshes</a> <b>[C]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ryan S. 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