@Article{IJNAM-2-3,
author = {Peszynska, Malgorzata},
title = {Mortar Adaptivity in Mixed Methods for Flow in Porous Media},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2005},
volume = {2},
number = {3},
pages = {241--282},
abstract = {<p style="text-align: justify;">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 Lagrange multipliers
defined as continuous piecewise linears on the subdomain interface. 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 2D flow problems with diagonal
coefficients for $\rm{RT}_{[0]}$ 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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2005-IJNAM-931},
url = {https://global-sci.com/article/83858/mortar-adaptivity-in-mixed-methods-for-flow-in-porous-media}
}