Volume 8, Issue 2
Optimal Error Estimates of the Local Discontinuous Galerkin Method for Willmore Flow of Graphs on Cartesian Meshes
DOI:

Int. J. Numer. Anal. Mod., 8 (2011), pp. 252-283

Published online: 2011-08

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• Abstract

In this paper, we analyze a local discontinuous Galerkin method for the willmore flow of graphs. We derive the optimal error estimates for this nonlinear equation in one-dimension and in multi-dimensions for Cartesian meshes using completely discontinuous piecewise polynomial space with degree $k \leq 1$.

• Keywords

local discontinuous Galerkin method Willmore flow of graphs stability error estimates

• AMS Subject Headings

65M60 35K55