Mesh grading in isogeometric analysis

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• 作者：Ulrich Langer ^{ulrich.langer@ricam.oeaw.ac.at" class="auth_mail" title="E-mail the corresponding author} ; Angelos Mantzaflaris ^{angelos.mantzaflaris@oeaw.ac.at" class="auth_mail" title="E-mail the corresponding author} ; Stephen E. Moore ^{stephen.moore@ricam.oeaw.ac.at" class="auth_mail" title="E-mail the corresponding author} ; Ioannis Toulopoulos ; ^{ioannis.toulopoulos@oeaw.ac.at" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Elliptic boundary value problems ; Domains with geometric singular points or edges ; Discontinuous coefficients ; Isogeometric analysis ; Mesh grading ; Recovering optimal convergence rates
• 刊名：Computers & Mathematics with Applications
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：70
• 期：7
• 页码：1685-1700
• 全文大小：1365 K

文摘

This paper is concerned with the construction of graded meshes for approximating so-called singular solutions of elliptic boundary value problems by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes. Such solutions appear, for instance, in domains with re-entrant corners on the boundary of the computational domain, in problems with changing boundary conditions, in interface problems, or in problems with singular source terms. Making use of the analytic behavior of the solution, we construct the graded meshes in the neighborhoods of such singular points following a multipatch approach. We prove that appropriately graded meshes lead to the same convergence rates as in the case of smooth solutions with approximately the same number of degrees of freedom. Representative numerical examples are studied in order to confirm the theoretical convergence rates and to demonstrate the efficiency of the mesh grading technology in Isogeometric Analysis.