Optimal Error Estimates of the Local Discontinuous Galerkin Method for Surface Diffusion of Graphs on Cartesian Meshes |
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Authors: | Liangyue Ji Yan Xu |
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Affiliation: | 1. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China 2. Delft Institute of Applied Mathematics, Delft University of Technology, 2628, CD, Delft, The Netherlands
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Abstract: | In (Xu and Shu in J. Sci. Comput. 40:375–390, 2009), a local discontinuous Galerkin (LDG) method for the surface diffusion of graphs was developed and a rigorous proof for
its energy stability was given. Numerical simulation results showed the optimal order of accuracy. In this subsequent paper,
we concentrate on analyzing a priori error estimates of the LDG method for the surface diffusion of graphs. The main achievement is the derivation of the optimal
convergence rate k+1 in the L
2 norm in one-dimension as well as in multi-dimensions for Cartesian meshes using a completely discontinuous piecewise polynomial
space with degree k≥1. |
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