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In this paper, the algorithms of the automatic mesh generator NETGEN are described. The domain is provided by a Constructive Solid Geometry (CSG). The whole task of 3D mesh generation splits into four subproblems of special point calculation, edge following, surface meshing and finally volume mesh generation. Surface and volume mesh generation are based on… (More)

- Joachim Schöberl
- Math. Comput.
- 2008

Maxwell equations are posed as variational boundary value problems in the function space H(curl) and are discretized by Nédélec finite elements. In Beck et al., 2000, a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain. In the present paper, we prove the reliability of that error estimator on… (More)

- Zdenek Dostál, Joachim Schöberl
- Comp. Opt. and Appl.
- 2005

A new active set based algorithm is proposed that uses the conjugate gradient method to explore the face of the feasible region defined by the current iterate and the reduced gradient projection with the fixed steplength to expand the active set. The precision of approximate solutions of the auxiliary unconstrained problems is controlled by the norm of… (More)

- Stefan Reitzinger, Joachim Schöberl
- Numerical Lin. Alg. with Applic.
- 2002

This paper presents an algebraic multigrid method for the e cient solution of the linear system arising from a nite element discretization of variational problems in H0(curl; ). The nite element spaces are generated by N ed elec’s edge elements. A coarsening technique is presented, which allows the construction of suitable coarse nite element spaces,… (More)

- Dietrich Braess, Joachim Schöberl
- Math. Comput.
- 2008

Reliable a posteriori error estimates without generic constants can be obtained by a comparison of the finite element solution with a feasible function for the dual problem. A cheap computation of such functions via equilibration is well known for scalar equations of second order. We simplify and modify the equilibration such that it can be applied to the… (More)

- Joachim Schöberl, Walter Zulehner
- SIAM J. Matrix Analysis Applications
- 2007

We consider large scale sparse linear systems in saddle point form. A natural property of such indefinite 2-by-2 block systems is the positivity of the (1,1) block on the kernel of the (2,1) block. Many solution methods, however, require that the positivity of the (1,1) block is satisfied everywhere. To enforce the positivity everywhere, an augmented… (More)

- Joachim Schöberl
- Numerische Mathematik
- 1999

In this paper we consider multigrid methods for the parameter dependent problem of nearly incompressible materials. We construct and analyze multilevel-projection algorithms, which can be applied to the mixed as well as to the equivalent, non-conforming nite element scheme in primal variables. For proper norms, we prove that the smoothing property and the… (More)

Equilibrated residual error estimators applied to high order finite elements are analyzed. The estimators provide always a true upper bound for the energy error. We prove that also the efficiency estimate is robust with respect to the polynomial degrees. The result is complete for tensor product elements. In the case of simplicial elements, the theorem is… (More)

The goal of the presented work is the efficient computation of Maxwell boundary and eigenvalue problems using high order H(curl) finite elements. We discuss a systematic strategy for the realization of arbitrary order hierarchic H(curl)conforming finite elements for triangular and tetrahedral element geometries. The shape functions are classified as… (More)

Consider the tangential trace of a vector polynomial on the surface of a tetrahedron. We construct an extension operator that extends such a trace function into a polynomial on the tetrahedron. This operator can be continuously extended to the trace space of H(curl ). Furthermore, it satisfies a commutativity property with an extension operator we… (More)