  This article proposes modifications to standard low order finite element
approximations of the Stokes system with the goal of improving both the
approximation quality and the parallel algebraic solution process. Different
from standard finite element techniques, we do not modify or enrich the
approximation spaces but modify the operator itself to ensure fundamental
physical properties such as mass and energy conservation. Special local
a~priori correction techniques at re-entrant corners lead to an improved
representation of the energy in the discrete system and can suppress the global
pollution effect. Local mass conservation can be achieved by an a~posteriori
correction to the finite element flux. This avoids artifacts in coupled
multi-physics transport problems. Finally, hardware failures in large
supercomputers may lead to a loss of data in solution subdomains. Within
parallel multigrid, this can be compensated by the accelerated solution of
local subproblems. These resilient algorithms will gain importance on future
extreme scale computing systems.
