arXiv subjects

Michael Lantelme

Publications and source records attributed to Michael Lantelme.

3 recordsLinked to original sources

arXiv2026

A posteriori error estimates for parabolic PDEs on evolving surfaces

We derive residual-based a posteriori error estimates for parabolic surface PDEs on closed evolving surfaces. The main contribution is to prove efficiency and reliability for the proposed error indicator, which bounds the error quantities globally from above and globally in space and locally in time from below. We extend methods for adaptivity for parabolic PDEs on stationary surfaces to allow for non-trivial coarsening on evolving surfaces. Multiple numerical experiments are given, which illustrate the asymptotic behaviour of the error and effectiveness of the refinement and coarsening.

math.NA↗

arXiv2026

$\ell$FEM: An efficient loop-free Matlab implementation of isoparametric bulk and surface finite elements

The $\ell$FEM MATLAB package provides a simple, efficient, and flexible implementation of isoparametric finite elements in bulk domains and on surfaces. The finite element matrix assemblies are based on MATLAB's paged operators and therefore completely loop-free. We give a short and conscious description of high-order isoparametric surface finite elements, which is then used to describe the assembly process and the implementation. We report on relevant numerical experiments (runtime comparisons, modifications for non-linear problems, etc.), and on additional functions, examples, and a testing unit which are all part of the $\ell$FEM package.

math.NA↗

arXiv2026

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

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.

math.NA↗