610 research outputs found
Residual-based stabilized higher-order FEM for advection-dominated problems
No full textWe reconsider the numerical solution of linear(ized) advection-diffusion-reaction problems using higher-order finite elements together with stabilized Galerkin methods of streamline-diffusion type (SUPG) and with shock-capturing stabilization. The analysis improves the a priori analysis in our previous paper [T. Knopp, G. Lube, G. Rapin, Stabilized finite element methods with shock capturing for advection-diffusion problems, Comput. Methods Appl. Mech. Engrg. 191 (2002) 2997-3013]. The theoretical results are supported by some numerical experiments. (c) 2005 Elsevier B.V. All rights reserved
A stabilized three-field formulation for advection-diffusion equations
No full textIn this paper, we propose a new stabilized three-field formulation applied to the advection-diffusion equation. Using finite elements with SUPG stabilization in the interior of the subdomains our approach enables LIS to use almost arbitrary discrete function spaces. They need not to satisfy the inf-sup conditions of the standard three-field formulation. We can prove the stability of the scheme and an I priori estimate which is of the same convergence order as the standard SUPG method. Furthermore, the scheme can be solved efficiently by an adapted Schur complement equation. Finally some numerical experiments confirm our theoretical results
A stabilized scheme for the lagrange multiplier method for advection-diffusion equations
No full textWe consider a new stabilized finite element method for advection-diffusion equations, where the Dirichlet boundary condition is imposed in a weak sense by Lagrange multipliers. The inf-sup condition of the corresponding mixed problem is circumvented by adding some further terms. Using the SUPG-stabilization, an optimal a priori estimate is shown for the singularly perturbed case. Then we present an a posteriori error estimator for our stabilized scheme. Some numerical experiments support the theoretical results. The present results are basic for a nonconforming three-field formulation of the problem
Residual-based stabilized higher-order fem for a generalized Oseen problem
No full textIn many numerical schemes for standard turbulence models for the nonstationary, incompressible Navier-Stokes equations, the problem is split into linearized auxiliary problems of advection-diffusion-reaction and of Oseen type. Here we present the numerical analysis of a conforming hp-version for stabilized Galerkin methods of SUPG/PSPG-type of the latter problem whereas the analysis of the former problem is reviewed in Ref. 22. We prove a modified inf-sup condition with a constant, which is independent of the spectral order and the viscosity. Moreover, the analysis of the stabilization parameters highlights the role of grad-div stabilization, in particular in case of div-stable velocity-pressure approximation
Stabilized FEM with shock-capturing for advection-diffusion problems
No full textStabilized FEM of streamline-diffusion type to advection-diffusion problems may exhibit local oscillations in crosswind direction(s). As a remedy, a shock-capturing variant is considered as an additional consistent (but nonlinear) stabilization. We present some preliminary results of the numerical analysis. The shock-capturing method has been applied within the numerical solution of the k/epsilon turbulence model of incompressible flow problems for the arising nonlinear advection-diffusion problems
Stabilized finite element methods with shock capturing for advection-diffusion problems
No full textStabilized FEM of streamline-diffusion type for advection-diffusion problems may exhibit local oscillations in crosswind direction(s). As a remedy, a shock-capturing variant of such stabilized schemes is considered as an additional consistent (but nonlinear) stabilization. We prove existence of discrete solutions. Then we present some a priori and a posteriori estimates. Finally we address the efficient solution of the arising nonlinear discrete problems. (C) 2002 Elsevier Science B.V. All rights reserved
Local projection stabilization for incompressible flows: Equal-order vs. inf-sup stable interpolation
No full textA standard approach to the non-stationary, incompressible Navier-Stokes model is to split the problem into linearized auxiliary problems of Oseen type. In this paper, a unified numerical analysis for finite element discretizations using the local projection stabilization method with either equal-order or inf-sup stable velocity-pressure pairs in the case of continuous pressure approximation is presented. Moreover, a careful comparison of both variants is given
Local projection stabilization for incompressible flows: Equal-order vs. inf-sup stable interpolation
No full textA standard approach to the non-stationary, incompressible Navier-Stokes model is to split the problem into linearized auxiliary problems of Oseen type. In this paper, a unified numerical analysis for finite element discretizations using the local projection stabilization method with either equal-order or inf-sup stable velocity-pressure pairs in the case of continuous pressure approximation is presented. Moreover, a careful comparison of both variants is given
DERIVING A NEW DOMAIN DECOMPOSITION METHOD FOR THE STOKES EQUATIONS USING THE SMITH FACTORIZATION
No full textIn this paper the Smith factorization is used systematically to derive a new domain decomposition method for the Stokes problem. In two dimensions the key idea is the transformation of the Stokes problem into a scalar bi-harmonic problem. We show, how a proposed domain decomposition method for the bi-harmonic problem leads to a domain decomposition method for the Stokes equations which inherits the convergence behavior of the scalar problem. Thus, it is sufficient to study the convergence of the scalar algorithm. The same procedure can also be applied to the three-dimensional Stokes problem. As transmission conditions for the resulting domain decomposition method of the Stokes problem we obtain natural boundary conditions. Therefore it can be implemented easily. A Fourier analysis and some numerical experiments show very fast convergence of the proposed algorithm. Our algorithm shows a more robust behavior than Neumann-Neumann or FETI type methods
Stabilized FEM with shock-capturing for advection-diffusion problems
No full textStabilized FEM of streamline-diffusion type to advection-diffusion problems may exhibit local oscillations in crosswind direction(s). As a remedy, a shock-capturing variant is considered as an additional consistent (but nonlinear) stabilization. We present some preliminary results of the numerical analysis. The shock-capturing method has been applied within the numerical solution of the k/epsilon turbulence model of incompressible flow problems for the arising nonlinear advection-diffusion problems
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