Mortar adaptivity in mixed methods for flow in porous media
Malgorzata Peszynska 11 Department of Mathematics, Oregon State University Corvallis, OR 97330, USA
Received by the editors April 15, 2004 and, in revised form, October 22, 2004
We define an error indicator for mixed mortar formulation of flow in porous media. The mixed mortar domain decomposition method for single phase flow problems was defined by Arbogast et al; it relies on coupling of subdomain problems using mortar La grange multipliers defined as continuous piecewise linears on the subdomain inter face. The accuracy and efficiency of the resulting interface formulation depends on the number of mortar degrees of freedom which we propose to adapt using error indicators involving jump of the flux across the interface. Rigorous a-posteriori analysis and proof of reliability of the estimator are established for single-phase 2 flow problems with diagonal coefficients for RT()spaces on rectangular grids. Computational experiments demonstrate the application of the estimator. Next, the algorithm and indicator are extended to the two-phase flow case which is illustrated with numerical examples. We focus on adapting the mortar grid while keeping subdomain grid fixed. Full mortar adaptivity is discussed elsewhere.
AMS subject classifications: 65N30, 65M60, 65N50, 65N55, 76S05, 76M10
Key words: single-phase flow in porous media; multi-phase flow; mixed finite elements; a-posteriori error estimation; mortars; domain decomposition; adaptvity