A fully discrete evolving surface finite element method

摘要

In this paper we consider a time discrete evolving surface finite element method for the advection and diffusion of a conserved scalar quantity on a moving surface. In earlier papers using a suitable variational formulation in time dependent Sobolev space we proposed and analyzed a finite element method using surface finite elements on evolving triangulated surfaces [IMA J. Numer Anal., 25(2007), pp. 385-407; Math. Comp., to appear]. Optimal order L~ 2(Γ(t)) and H~ 1(G(t)) error bounds were proved for linear finite elements. In this work we prove optimal order error bounds for a backward Euler time discretization.