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arXiv · 1602.04625

Stable discontinuous Galerkin FEM without penalty parameters

Lorenz John·Michael Neilan·Iain Smears
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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. 2016-03-09. Stable discontinuous Galerkin FEM without penalty parameters. https://doi.org/10.1007/978-3-319-39929-4_17

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