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An $$hp$$-analysis of the local discontinuous Galerkin method for diffusion problems. (English) Zbl 1001.76060
Summary: We present an $$hp$$-error analysis of local discontinuous Galerkin method for diffusion problems, considering unstructured meshes with hanging nodes in two- and three-dimensional domains. Our estimates are optimal in the mesh size $$h$$, and slightly suboptimal in the polynomial approximation order $$p$$. Optimality in $$p$$ is achieved by matching grids and polynomial boundary conditions.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 76R50 Diffusion
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