Stable Discontinuous Galerkin FEM Without Penalty Parameters

Lorenz John (1) , Michael Neilan (2) , Iain Smears (3)

1 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich
2 PITT - University of Pittsburgh
3 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms

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.

Domaines: Analyse numérique [math.NA]

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⟩