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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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