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Domain decomposition methods with adaptive mesh refinement for convection-reaction-diffusion problems

We construct an adaptive convergent algorithm type Uzawa using domain descomposition techniques, AMUADD, for solving 2nd order elliptic stationary problems and generalize the algorithm for Convection-Reaction-Diffusion problems and as well as a parallel version of the algorithm for a shared memory machines.

We are going to consider a linear stationary problem defined in a ? domain, decompose the domain into two subdomains ?1 and ?2, ?12 is the interface, and we apply on each subdomain an adaptive element finite method using an independent mesh refinement based on a posteriori error estimative.

The starting point is the Hybrid Primal formulation of an elliptic problem.

We modify the Uzawa algorithm in two ways: First we will use different auxiliary operators to solve the problem on the interface in order to accelerate convergence. Second, we introduce mesh adaptivity (Adaptive Modified Uzawa algorithm).
 
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