Volume 51, Number 5, September-October 2017
|Page(s)||1561 - 1581|
|Published online||27 September 2017|
An edge-based scheme on polyhedral meshes for vector advection-reaction equations
1 Université Paris-Est, CERMICS (ENPC), 77455 Marne la Vallée cedex 2, France.
2 EDF R&D, 6 quai Watier, BP 49, 78401 Chatou, France.
Received: 1 June 2016
Revised: 21 November 2016
Accepted: 28 November 2016
We devise and analyze an edge-based scheme on polyhedral meshes to approximate a vector advection-reaction problem. The well-posedness of the discrete problem is analyzed first under the classical positivity hypothesis of Friedrichs’ systems that requires a lower bound on the lowest eigenvalue of some tensor depending on the model parameters. We also prove stability when the lowest eigenvalue is null or even slightly negative if the mesh size is small enough. A priori error estimates are established for solutions in W1,q(Ω) with q ∈ ((3/2),2]. Numerical results are presented on three-dimensional polyhedral meshes.
Mathematics Subject Classification: 65N12 / 65N15 / 76R99 / 76D07 / 76W05
Key words: Vector advection-reaction problems / polyhedral meshes / Friedrichs’ assumptions / quasi-optimala priori error estimates
© EDP Sciences, SMAI 2017
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