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A two-dimensional moving finite element method with local refinement based on a posteriori error estimates. (English) Zbl 1022.65107
Summary: We consider the numerical solution of time-dependent partial differential equation (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.

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
Software:
RODAS; Kaskade7; PLTMG
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References:
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