Discontinuous Galerkin method for the solution of a transport level-set problem

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• 作者：Eva Bezchlebová ; Ví ; t Dolej&scaron ; í ; ; ^{dolejsi@karlin.mff.cuni.cz" class="auth_mail" title="E-mail the corresponding author} ; Miloslav Feistauer ^{feist@karlin.mff.cuni.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Transport equation ; Discontinuous Galerkin space discretization ; Space&ndash ; time discontinuous Galerkin method ; Error estimates ; Numerical experiments
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：72
• 期：3
• 页码：455-480
• 全文大小：1370 K

文摘

The subject of the paper is the numerical analysis of the transport level-set problem discretized by the discontinuous Galerkin method. Without the assumption that the first order nonstationary transport equation contains a reaction term, which is used in a standard literature, we prove error estimates in the L^∞(L²)$L^{\infty }\left(L^2\right)$-norm in the case of the space semidiscretization method of lines and in the case of the space–time discontinuous Galerkin method in the L²(L²)$L^2\left(L^2\right)$-norm. Numerical experiments support the derived error estimates and show that they are not sharp in the case of the space–time discontinuous Galerkin method.