High-order evolving surface finite element method for parabolic problems on evolving surfaces

摘要

High-order spatial discretizations and full discretizations 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 discretizations using backward difference formulae and implicit Runge-Kutta methods are also shown.