preprint Balázs Kovács author 1004410000-0001-9872-3474 Michael Frederik Raúl Lantelme author 102867 841 department 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 eng 2407.02101 Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error Estimates for Parabolic Partial Differential Equations on Stationary Surfaces.” <i>ArXiv:2407.02101</i>, 2024. @article{Kovács_Lantelme_2024, title={A posteriori error estimates for parabolic partial differential equations on stationary surfaces}, journal={arXiv:2407.02101}, author={Kovács, Balázs and Lantelme, Michael Frederik Raúl}, year={2024} } Kovács B, Lantelme MFR. A posteriori error estimates for parabolic partial differential equations on stationary surfaces. <i>arXiv:240702101</i>. Published online 2024. B. Kovács and M. F. R. Lantelme, “A posteriori error estimates for parabolic partial differential equations on stationary surfaces,” <i>arXiv:2407.02101</i>. 2024. Kovács, B., &#38; Lantelme, M. F. R. (2024). A posteriori error estimates for parabolic partial differential equations on stationary surfaces. In <i>arXiv:2407.02101</i>. B. Kovács, M.F.R. Lantelme, ArXiv:2407.02101 (2024). Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error Estimates for Parabolic Partial Differential Equations on Stationary Surfaces.” <i>ArXiv:2407.02101</i>, 2024. 550782024-07-04T12:53:47Z2026-02-18T14:45:36Z