High-order evolving surface finite element method for parabolic problems on evolving surfaces
Numerical Analysis
2016-06-24 v1
Abstract
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order versions of geometric approximation errors and perturbation error estimates and by the careful error analysis of a modified Ritz map. Furthermore, convergence of full discretisations using backward difference formulae and implicit Runge-Kutta methods are also shown.
Cite
@article{arxiv.1606.07234,
title = {High-order evolving surface finite element method for parabolic problems on evolving surfaces},
author = {Balázs Kovács},
journal= {arXiv preprint arXiv:1606.07234},
year = {2016}
}