Work

A Posteriori Error Estimates for Parabolic Partial Differential Equations on Stationary Surfaces

Year: 2026

Type: article

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.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/25m1784466

Authors: Balázs Kovács, Michael Lantelme

Institution: Paderborn University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: G1575401848, G371845181, Numerische Analysis von geometrischen Flüssen und partiellen Differentialgleichungen auf bewegten Oberflächen