TY - JOUR T1 - Optimal Error Estimates of the Local Discontinuous Galerkin Method for Willmore Flow of Graphs on Cartesian Meshes JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 252 EP - 283 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/685.html KW - local discontinuous Galerkin method, Willmore flow of graphs, stability, error estimates. AB -

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 $k \leq 1$.