A two-dimensional moving finite element method with local refinement based on a posteriori error estimates

Authors:
Jens Lang;Weiming Cao;Weizhang Huang;Robert D. Russell
Affiliations:
Department of Mathematics, Darmstadt University of Technology, Schlossgartenstr. 7, 64289 Darmstadt, Germany;Department of Applied Mathematics, The University of Texas at San Antonio, San Antonio, TX;Department of Mathematics, The University of Kansas, Lawrence, KS;Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
Venue:
Applied Numerical Mathematics
Year:
2003

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Abstract

In this paper, we consider the numerical solution of time-dependent PDEs using a finite element method based upon rh-adaptivity. An adaptive horizontal method of lines strategy equipped with a posteriori error estimates to control the discretization through variable time steps and spatial grid adaptations is used. Our approach combines an r-refinement method based upon solving so-called moving mesh PDEs with h-refinement. Numerical results are presented to demonstrate the capabilities and benefits of combining mesh movement and local refinement.