Parallel solvers for virtual element discretizations of elliptic equations in mixed form

Fast parallel solvers for symmetric boundary element domain decomposition equations

C. Carstensen1, M. Kuhn2, U. Langer3 1 Mathematical Seminar, Christian-Albrechts-University Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany; e-mail: [email protected] 2 Institute of Mathematics, Johannes Kepler University Linz, Altenberger Str. 69, A-4040 Linz, Austria; e-mail: [email protected] 3 Institute of Mathematics, Johannes Kepler University Linz, Altenberger Str. 69, A-404...

Finite Element Preconditioning on Spectral Element Discretizations for Coupled Elliptic Equations

Schwarz Type Solvers for hp-FEM Discretizations of Mixed Problems

The Stokes problem and linear elasticity problems can be viewed as a mixed variational formulation. These formulations are discretized by means of the hp-version of the finite element method. The system of linear algebraic equations is solved by the preconditioned Bramble-Pasciak conjugate gradient method. The development an efficient preconditioner requires three ingredients, a preconditioner ...

A posteriori error estimates for nonlinear problems. Lr-estimates for finite element discretizations of elliptic equations

— We extend the gênerai framework of [18] for deriving a posteriori error estimâtes for approximate solutions of noniinear elliptic problems such ihat it also yields L'-error estimâtes. The gênerai results are applied to finite element discretizations of scalar quasilinear elliptic pdes of 2nd order and the stationary incompressible Navier-Stokes équations. They immediately yield a posteriori e...

Boundary preconditioners for mixed finite-element discretizations of fourth-order elliptic problems

Abstract We extend the preconditioning approach of Glowinski and Pironneau, and of Peisker to the case of mixed finite element general fourth-order elliptic problems. We show that H−1/2-preconditioning on the boundary leads to mesh-independent performance of iterative solvers of Krylov subspace type. In particular, we show that the field of values of the boundary Schur complement preconditioned...