Maximum norm stability and error estimates for the evolving surface finite element method

Abstract

We show convergence in the natural $L^{\infty }$- and $W^{1,\infty }$-norm for a semidiscretization with linear finite elements of a linear parabolic partial differential equations on evolving surfaces. To prove this we show error estimates for a Ritz map, error estimates for the material derivative of a Ritz map and a weak discrete maximum principle.

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Cited by in corpus (1)

• Lumped finite element method for reaction-diffusion systems on compact surfaces