Stable Discontinuous Galerkin FEM Without Penalty Parameters

Abstract : We propose a modified local discontinuous Galerkin (LDG) method for second–order elliptic problems that does not require extrinsic penalization to ensure stability. Stability is instead achieved by showing a discrete Poincaré–Friedrichs inequality for the discrete gradient that employs a lifting of the jumps with one polynomial degree higher than the scalar approximation space. Our analysis covers rather general simplicial meshes with the possibility of hanging nodes.
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Lorenz John, Michael Neilan, Iain Smears. Stable Discontinuous Galerkin FEM Without Penalty Parameters. Numerical Mathematics and Advanced Applications ENUMATH 2015, Sep 2015, Ankara, Turkey. pp.XIV, 643, ⟨10.1007/978-3-319-39929-4_17⟩. ⟨hal-01428664⟩

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