Iterative Galerkin discretizations for strongly monotone problems

Efficient Iterative Solvers for Stochastic Galerkin Discretizations of Log-Transformed Random Diffusion Problems

We consider the numerical solution of a steady-state diffusion problem where the diffusion coefficient is the exponent of a random field. The standard stochastic Galerkin formulation of this problem is computationally demanding because of the nonlinear structure of the uncertain component of it. We consider a reformulated version of this problem as a stochastic convection-diffusion problem with...

Multigrid Algorithms for hp-Discontinuous Galerkin Discretizations of Elliptic Problems

We present W-cycle multigrid algorithms for the solution of the linear system of equations arising from a wide class of hp-version discontinuous Galerkin discretizations of elliptic problems. Starting from a classical framework in multigrid analysis, we define a smoothing and an approximation property, which are used to prove the uniform convergence of the W-cycle scheme with respect to the gra...

Convergence of Iterative Sequences for Generalized Equilibrium Problems Involving Inverse-Strongly Monotone Mappings

Preconditioning High-Order Discontinuous Galerkin Discretizations of Elliptic Problems

In recent years, attention has been devoted to the development of efficient iterative solvers for the solution of the linear system of equations arising from the discontinuous Galerkin (DG) discretization of a range of model problems. In the framework of two level preconditioners, scalable non-overlapping Schwarz methods have been proposed and analyzed for the h–version of the DG method in the ...

Algebraic Multigrid for Discontinuous Galerkin Discretizations

We present a new algebraic multigrid (AMG) algorithm for the solution of linear systems arising from discontinuous Galerkin discretizations of heterogeneous elliptic problems. The algorithm is based on the idea of subspace corrections and the first coarse level space is the subspace spanned by continuous linear basis functions. The linear system associated with this space is constructed algebra...