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Displaying similar documents to “Upwind FEM for convection dominated elliptic problems”

On the quality of local flux reconstructions for guaranteed error bounds

Vejchodský, Tomáš

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In this contribution we consider elliptic problems of a reaction-diffusion type discretized by the finite element method and study the quality of guaranteed upper bounds of the error. In particular, we concentrate on complementary error bounds whose values are determined by suitable flux reconstructions. We present numerical experiments comparing the performance of the local flux reconstruction of Ainsworth and Vejchodsky [2] and the reconstruction of Braess and Schöberl [5]. We evaluate...

Discontinuous Galerkin method for nonlinear convection-diffusion problems with mixed Dirichlet-Neumann boundary conditions

Oto Havle, Vít Dolejší, Miloslav Feistauer (2010)

Applications of Mathematics

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The paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion problem with mixed Dirichlet-Neumann boundary conditions. General nonconforming meshes are used and the NIPG, IIPG and SIPG versions of the discretization of diffusion terms are considered. The main attention is paid to the impact of the Neumann boundary condition prescribed on a part of the boundary...

Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems

Martin Kahlbacher, Stefan Volkwein (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Proper orthogonal decomposition (POD) is a powerful technique for model reduction of linear and non-linear systems. It is based on a Galerkin type discretization with basis elements created from the system itself. In this work, error estimates for Galerkin POD methods for linear elliptic, parameter-dependent systems are proved. The resulting error bounds depend on the number of POD basis functions and on the parameter grid that is used to generate the snapshots and to compute the POD...