A FULLY DISCRETE EVOLVING SURFACE FINITE ELEMENT METHOD

作者：Dziuk Gerhard^*; Elliott Charles M

来源：SIAM Journal on Numerical Analysis, 2012, 50(5): 2677-2694.

DOI：10.1137/110828642

• surface finite elements
• advection diffusion
• moving surface
• error analysis

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(Gamma(t)) and H-1(Gamma(t)) error bounds were proved for linear finite elements. In this work we prove optimal order error bounds for a backward Euler time discretization.

• 出版日期2012