Stable discontinuous Galerkin FEM without penalty parameters
arXiv:1602.04625 · doi:10.1007/978-3-319-39929-4_17
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.
Accepted for publication in the conference proceedings of Numerical Mathematics and Advanced Applications ENUMATH 2015. Typo corrected
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