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This article proposes modifications to standard low order finite elementapproximations of the Stokes system with the goal of improving both theapproximation quality and the parallel algebraic solution process. Differentfrom standard finite element techniques, we do not modify or enrich theapproximation spaces but modify the operator itself to ensure fundamentalphysical properties such as mass and energy conservation. Special locala~priori correction techniques at re-entrant corners lead to an improvedrepresentation of the energy in the discrete system and can suppress the globalpollution effect. Local mass conservation can be achieved by an a~posterioricorrection to the finite element flux. This avoids artifacts in coupledmulti-physics transport problems. Finally, hardware failures in largesupercomputers may lead to a loss of data in solution subdomains. Withinparallel multigrid, this can be compensated by the accelerated solution oflocal subproblems. These resilient algorithms will gain importance on futureextreme scale computing systems.

Solution Techniques for the Stokes System: A priori and a posteriori modifications, resilient algorithms