- Volume 21 Issue 5
A new a posteriori error estimator is introduced and applied to variational inequalities occurring in problems of flow through porous media. In order to construct element-wise a posteriori error estimates the global error is localized by a special mixed formulation in which continuity conditions at interfaces are treated as constraints. This approach leads to error indicators which provide rigorous upper bounds of the element errors. A discussion of a compatibility condition for the well-posedness of the local error analysis problem is given. Two numerical examples are solved to check the compatibility of the local problems and convergence of the effectivity index both in a local and a global sense with respect to local refinements.
Variational Inequalities;Finite Element Approximation;A Posteriori Error;Minimization Problem;Global Error;Local Error;Error Estimation;Porous Media