Abstract
We present an hp-error analysis of the local discontinuous Galerkin method for diffusion problems, considering unstructured meshes with hanging nodes and two- and three-dimensional domains. Our estimates are optimal in the meshsize h and slightly suboptimal in the polynomial approximation order p. Optimality in p is achieved for matching grids and polynomial boundary conditions.
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Perugia, I., Schötzau, D. An hp-Analysis of the Local Discontinuous Galerkin Method for Diffusion Problems. Journal of Scientific Computing 17, 561–571 (2002). https://doi.org/10.1023/A:1015118613130
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DOI: https://doi.org/10.1023/A:1015118613130