Ralf Kornhuber

A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE

In a companion paper (Bastian et al. 2007, this issue) we introduced an abstract definition of a parallel and adaptive hierarchical grid for scientific computing. Based on this definition we derive an efficient interface specification as a set of C++ classes. This interface separates the applications from the grid data structures. Thus, user implementations become independent of the underlying grid implementation. Modern C++ template techniques are used to provide an interface implementation without big performance losses. The implementation is realized as part of the software environment DUNE (http://dune-project.org/). Numerical tests demonstrate the flexibility and the efficiency of our approach.

A posteriori error estimates for elliptic problems in two and three space dimensions

Let

Adaptive multilevel methods for obstacle problems

u \in H

A posteriori error estimates for elliptic variational inequalities

be the exact solution of a given selfadjoint elliptic boundary value problem, which is approximated by some

On adaptive grid refinement in the presence of internal or boundary layers

\tilde u \in \mathcal{S}

On constrained Newton linearization and multigrid for variational inequalities

,

Fast and Robust Numerical Solution of the Richards Equation in Homogeneous Soil

\mathcal{S}

Hierarchical error estimates for the energy functional in obstacle problems

being a suitable finite-element space. Efficient and reliable a posteriors estimates of the error

Nonsmooth Newton Methods for Set-Valued Saddle Point Problems

\| {u - \tilde u} \|

On Preconditioned Uzawa-type Iterations for a Saddle Point Problem with Inequality Constraints

, measuring the (local) quality of