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Generalization of the Zlámal condition for simplicial finite elements in d

Jan Brandts, Sergey Korotov, Michal Křížek (2011)

Applications of Mathematics

The famous Zlámal’s minimum angle condition has been widely used for construction of a regular family of triangulations (containing nondegenerating triangles) as well as in convergence proofs for the finite element method in 2 d . In this paper we present and discuss its generalization to simplicial partitions in any space dimension.

Generalizations of the Finite Element Method

Marc Schweitzer (2012)

Open Mathematics

This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical method. To...

Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems

Vít Dolejší, Filip Roskovec (2017)

Applications of Mathematics

We deal with a posteriori error control of discontinuous Galerkin approximations for linear boundary value problems. The computational error is estimated in the framework of the Dual Weighted Residual method (DWR) for goal-oriented error estimation which requires to solve an additional (adjoint) problem. We focus on the control of the algebraic errors arising from iterative solutions of algebraic systems corresponding to both the primal and adjoint problems. Moreover, we present two different reconstruction...

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