Maximum norm stability and error estimates for the evolving surface finite element method
arXiv:1510.0060513 citationsh-index: 10
Originality Incremental advance
AI Analysis
Provides rigorous maximum-norm error analysis for evolving surface finite element methods, addressing a gap in numerical analysis for moving domains.
The paper proves convergence in the maximum norm for linear finite element discretization of parabolic PDEs on evolving surfaces, establishing error estimates and a weak discrete maximum principle.
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.