Skip to Main content Skip to Navigation
New interface
Journal articles

Stabilized Galerkin for transient advection of differential forms

Abstract : We deal with the discretization of generalized transient advection problems for differential forms on bounded spatial domains. We pursue an Eulerian method of lines approach with explicit timestepping. Concerning spatial discretization we extend the jump stabilized Galerkin discretization proposed in [ H. HEUMANN and R.HIPTMAIR, Stabilized Galerkin methods for magnetic advection, Math. Modelling Numer. Analysis, 47 (2013), pp.1713--1732] to forms of any degree and, in particular, advection velocities that may have discontinuities resolved by the mesh. A rigorous a priori convergence theory is established for Lipschitz continuous velocities, conforming meshes and standard finite element spaces of discrete differential forms. However, numerical experiments furnish evidence of the good performance of the new method also in the presence of jumps of the advection velocity.
Document type :
Journal articles
Complete list of metadata

Cited literature [39 references]  Display  Hide  Download
Contributor : Holger Heumann Connect in order to contact the contributor
Submitted on : Thursday, December 8, 2016 - 11:56:41 AM
Last modification on : Thursday, August 4, 2022 - 4:58:36 PM
Long-term archiving on: : Tuesday, March 21, 2017 - 3:07:22 AM


Files produced by the author(s)




Holger Heumann, Ralf Hiptmair, Cecilia Pagliantini. Stabilized Galerkin for transient advection of differential forms. Discrete and Continuous Dynamical Systems - Series S, 2016, 9 (1), pp.185 - 214. ⟨10.3934/dcdss.2016.9.185⟩. ⟨hal-01248140⟩



Record views


Files downloads