Carsten Carstensen

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A computable error bound for mixed finite element methods is established in the model case of the Poisson–problem to control the error in the H(div,Ω) ×L2(Ω)–norm. The reliable and efficient a posteriori error estimate applies, e.g., to Raviart–Thomas, Brezzi-Douglas-Marini, and Brezzi-DouglasFortin-Marini elements. 1. Mixed method for the Poisson problem(More)
A short Matlab implementation for P 1-x 1 finite elements on triangles and parallelograms is provided for the numerical solution of elliptic problems with mixed boundary conditions on unstructured grids. According to the shortness of the program and the given documentation, any adaptation from simple model examples to more complex problems can easily be(More)
A short Matlab implementation for P 1 and Q 1 finite elements (FE) is provided for the numerical solution of 2d and 3d problems in linear elasticity with mixed boundary conditions. Any adaptation from the simple model examples provided to more complex problems can easily be performed with the given documentation. Numerical examples with postprocessing and(More)
The interval version of the complex third-order method of Maehly, Borsch-Supan, Ehrlich, and Aberth is the most efficient method for simultaneous inclusion of simple polynomial roots [14]. In this note, Gargantini’s generalization of this third-order interval method for multiple roots is accelerated using Schroder’s modification of Newton’s corrections and(More)
Averaging techniques are popular tools in adaptive finite element methods since they provide efficient a posteriori error estimates by a simple postprocessing. In the second paper of our analysis of their reliability, we consider conforming h-FEM of higher (i.e., not of lowest) order in two or three space dimensions. In this paper, reliablility is shown for(More)
— We introducé two a posteriori error estimators for piecewise îinear nonconforming finit e element approximation of second order e Hipt ie problems. We prove that these estimators are equivalent to the energy norm of the error, Finally, we present several numerical experiments showing the good behavior of the estimators when they are used as local error(More)
The direct numerical solution of a non-convex variational problem (P ) typically faces the difficulty of the finite element approximation of rapid oscillations. Although the oscillatory discrete minimisers are properly related to corresponding Young measures and describe real physical phenomena, they are costly and difficult to compute. In this work, we(More)