Arbitrary dimension convection-diffusion schemes for space-time discretizations

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• 作者：Randolph E. Bank^a ; ^{rbank@ucsd.edu" class="auth_mail" title="E-mail the corresponding author} ; Panayot S. Vassilevski^b ; ^{panayot@llnl.gov" class="auth_mail" title="E-mail the corresponding author} ; Ludmil T. Zikatanov^c ; ^d ; ^{ludmil@psu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Space&ndash ; time formulation ; Convection&ndash ; diffusion problems ; Finite-element method ; Exponential fitting ; Streamline-diffusion
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：310
• 期：Complete
• 页码：19-31
• 全文大小：704 K

文摘

This note proposes embedding a time dependent PDE into a convection–diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average finite element) one, are investigated in terms of stability and error analysis. The EAFE scheme, in particular, is extended to be arbitrary order which is of interest on its own. Numerical results, in combined space–time domain demonstrate the feasibility of the proposed approach.