Space-time isogeometric analysis of parabolic evolution problems

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• 作者：Ulrich Langer^a ; ^{ulrich.langer@ricam.oeaw.ac.at" class="auth_mail" title="E-mail the corresponding author} ; Stephen E. Moore^a ; ^{stephen.moore@ricam.oeaw.ac.at" class="auth_mail" title="E-mail the corresponding author} ; Martin Neumü ; ller^b ; ^{neumueller@numa.uni-linz.ac.at" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35K20 ; 65M15 ; 65M60 ; 65M55
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2016
• 出版时间：1 July 2016
• 年：2016
• 卷：306
• 期：Complete
• 页码：342-363
• 全文大小：1220 K

文摘

We present and analyze a new stable space–time Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the IgA space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields an a priori discretization error estimate with respect to the discrete norm. The theoretical results are confirmed by several numerical experiments with low- and high-order IgA spaces.