Streamline diffusion finite element method for quasilinear elliptic problems.
G. Lube (1992)
Numerische Mathematik
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Displaying similar documents to “Upwind FEM for convection dominated elliptic problems”
Streamline diffusion finite element method for quasilinear elliptic problems.
A priori diffusion-uniform error estimates for singularly perturbed problems: Midpoint-DG discretization
Vlasák, Miloslav, Kučera, Václav
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We deal with a nonstationary semilinear singularly perturbed convection–diffusion problem. We discretize this problem by discontinuous Galerkin method in space and by midpoint rule in time. We present diffusion–uniform error estimates with sketches of proofs.
Pointwise Error Estimates for a Streamline Diffusion Finite Element Scheme.
Koichi Niijima (1989/90)
Numerische Mathematik
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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...
On the numerical solutions of convection-diffusion equations
O. Axelsson (1984)
Banach Center Publications
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Interior penalty discontinuous approximations of elliptic problems.
Lazarov, R., Tomov, S., Vassilevski, P. (2001)
Computational Methods in Applied Mathematics
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Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
Konstantinos Chrysafinos, Sotirios P. Filopoulos, Theodosios K. Papathanasiou (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
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Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity...