Publication Details

Category Text Publication
Reference Category Journals
DOI 10.1002/fld.1787
Title (Primary) Convergence of MPFA on triangulations and for Richards' equation
Author Klausen, R.A.; Radu, F.A.; Eigestad, G.T.
Journal International Journal for Numerical Methods in Fluids
Year 2008
Department CHS
Volume 58
Issue 12
Page From 1327
Page To 1351
Language englisch
Keywords Richards' equation; error estimates; mixed finite element method; multi-point flux approximation
Abstract Spatial discretization of transport and transformation processes in porous media requires techniques that handle general geometry, discontinuous coefficients and are locally mass conservative. Multi-point flux approximation (MPFA) methods are such techniques, and we will here discuss some formulations on triangular grids with further application to the nonlinear Richards equation. The MPFA methods will be rewritten to mixed form to derive stability conditions and error estimates. Several MPFA versions will be shown, and the versions will be discussed with respect to convergence, symmetry and robustness when the grids are rough. It will be shown that the behavior may be quite different for challenging cases of skewness and roughness of the simulation grids. Further, we apply the MPFA discretization approach for the Richards equation and derive new error estimates without extra regularity requirements. The analysis will be accompanied by numerical results for grids that are relevant for practical simulation. Copyright © 2008 John Wiley & Sons, Ltd.
Persistent UFZ Identifier
Klausen, R.A., Radu, F.A., Eigestad, G.T. (2008):
Convergence of MPFA on triangulations and for Richards' equation
Int. J. Numer. Methods Fluids 58 (12), 1327 - 1351