A convergent time-space adaptive dG(s) finite element method for parabolic problems motivated by equal error distribution

2016/10/21 by Gaspoz, Fernando, Kreuzer, Christian, Siebert, Kunibert +1 · 6 citations
#65N12 #65N15 #65N30 #65N50 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1610.06814

Abstract

We shall develop a fully discrete space-time adaptive method for linear parabolic problems based on new reliable and efficient a posteriori analysis for higher order dG(s) finite element discretisations. The adaptive strategy is motivated by the principle of equally distributing the a posteriori indicators in time and the convergence of the method is guaranteed by the uniform energy estimate from [KreuzerMöllerSchmidtSiebert:12] under minimal assumptions on the regularity of the data.

Cited by

• Optimal Time-Adaptivity for Parabolic Problems with applications to Model Order Reduction
• An introduction to the a posteriori error analysis of parabolic partial differential equations
• A posteriori error analysis and adaptivity of a space-time finite element method for the wave equation in second order formulation
• On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm
• Adaptive FEM with explicit time integration for the wave equation
• Optimal adaptive implicit time stepping

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