A posteriori error estimates for parabolic partial differential equations on stationary surfaces Kovács, Balázs Lantelme, Michael Frederik Raúl This paper develops and discusses a residual-based a posteriori error estimate and a space--time adaptive algorithm for solving 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. A space--time adaptive algorithm is proposed using the derived error indicator. Numerical experiments illustrate and complement the theory. 2024 info:eu-repo/semantics/preprint doc-type:preprint text http://purl.org/coar/resource_type/c_816b https://ris.uni-paderborn.de/record/55078 Kovács B, Lantelme MFR. A posteriori error estimates for parabolic partial differential equations on stationary surfaces. <i>arXiv:240702101</i>. Published online 2024. eng info:eu-repo/semantics/altIdentifier/arxiv/2407.02101 info:eu-repo/semantics/closedAccess