Optimal Error Estimates of the Local Discontinuous Galerkin Method for Surface Diffusion of Graphs on Cartesian Meshes

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...

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Bibliographic Details
Published in:Journal of scientific computing 2012-04, Vol.51 (1), p.1-27
Main Authors: Ji, Liangyue, Xu, Yan
Format: Article
Language:English
Subjects:
Algorithms
Cartesian coordinates
Computational Mathematics and Numerical Analysis
Error analysis
Estimates
Galerkin method
Graphs
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Polynomials
Surface diffusion
Theoretical
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Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-011-9492-4