A posteriori error estimates for parabolic partial differential equations on stationary surfaces

2024/07/02 by Balázs Kovács, Michael Lantelme, Kovács, Balázs +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2407.02101

openalex publication_date 2024/07/02 · openalex created_date 2024/07/06 · openalex updated_date 2026/08/01

Abstract

This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and the backward Euler method in time. The proposed error indicator bounds the error quantities globally in space from above and below, and globally in time from above and locally from below. Based on the derived error indicator, a space-time adaptive algorithm is proposed. Numerical experiments illustrate and complement the theory.

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