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

2015/10/02 by Kovács, Balázs, Guerra, Chrisitan Andreas Power
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1510.00605

Abstract

We show convergence in the natural L^∞- and W^1,∞-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.

Related

• Error analysis for full discretizations of quasilinear parabolic\n problems on evolving surfaces
• Maximal regularity of evolving FEMs for parabolic equations on an evolving surface
• Convergence of finite elements on an evolving surface driven by\n diffusion on the surface
• High-order evolving surface finite element method for parabolic problems\n on evolving surfaces
• Error analysis of a space-time finite element method for solving PDEs on\n evolving surfaces