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• W2895816528 abstract "We provide a short introduction to the theory of M-decompositions in the framework of steady-state diffusion problems. This theory allows us to systematically devise hybridizable discontinuous Galerkin and mixed methods which can be proven to be superconvergent on unstructured meshes made of elements of a variety of shapes. The main feature of this approach is that it reduces such an effort to the definition, for each element K of the mesh, of the spaces for the flux, V (K), and the scalar variable, W(K), which, roughly speaking, can be decomposed into suitably chosen orthogonal subspaces related to the space traces on ∂K of the scalar unknown, M(∂K). We begin by showing how a simple a priori error analysis motivates the notion of an M-decomposition. We then study the main properties of the M-decompositions and show how to actually construct them. Finally, we provide many examples in the two-dimensional setting. We end by briefly commenting on several extensions including to other equations like the wave equation, the equations of linear elasticity, and the equations of incompressible fluid flow." @default.
• W2895816528 created "2018-10-26" @default.
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• W2895816528 date "2018-01-01" @default.
• W2895816528 modified "2023-09-27" @default.
• W2895816528 title "An Introduction to the Theory of M-Decompositions" @default.
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• W2895816528 doi "https://doi.org/10.1007/978-3-319-94676-4_2" @default.
• W2895816528 hasPublicationYear "2018" @default.
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