Ronald H. W. Hoppe

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We consider mixed finite element discretizations of linear second order elliptic boundary value problems with respect to an adaptively generated hierarchy of possibly highly nonuniform simplicial triangulations. In particular, we present and analyze four different kinds of error estimators: a residual based estimator, a hierarchical one, error estimators(More)
An adaptive mixed finite element method (AMFEM) is designed to guarantee an error reduction, also known as saturation property: after each refinement step, the error for the fine mesh is strictly smaller than the error for the coarse mesh up to oscillation terms. This error reduction property is established here for the Raviart–Thomas finite element method(More)
The focus of this paper is on the eecient solution of boundary value problems involving the double{curl operator. Those arise in the computation of electromagnetic elds in various settings, for instance when solving the electric or magnetic wave equation with implicit timestepping, when tackling time{harmonic problems or in the context of eddy{current(More)
We are concerned with an a posteriori error analysis of adaptive finite element approximations of boundary control problems for second order elliptic boundary value problems under bilateral bound constraints on the control which acts through a Neumann type boundary condition. In particular, the analysis of the errors in the state, the adjoint state, the(More)
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A posteriori analysis has become an inherent part of numerical mathematics. Methods of a posteriori error estimation for finite element approximations were actively developed in the last two decades (see, e.g., [1, 2, 3, 13] and references therein). For problems in the theory of optimization these methods started receiving attention much later. In(More)