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- Hansbo, Peter F G, 1959, et al.
(author)
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A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations
- 1990
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In: Computer Methods in Applied Mechanics and Engineering. - LAUSANNE : Elsevier BV. ; 84:2, s. 175-192
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Journal article (peer-reviewed)abstract
- In this paper a streamline diffusion finite element method is introduced for the time-dependent incompressible Navier-Stokes equations in a bounded domnain in R^2 and R^3 in the case of high Reynolds number flow. An error estimate is proved and numerical results are given. The method is based on a mixed velocity-pressure formulation using the same finite element discretization of space-time for the velocity and the pressure spaces, which consists of piecewise linear functions, together with certain least-squares modifications of the Galerkin variational formulation giving added stability without sacrificing accuracy.
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- Johnson, Claes, et al.
(author)
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On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws
- 1990
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In: Mathematics of Computation. - PROVIDENCE : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 54:189, s. 107-129
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Journal article (peer-reviewed)abstract
- We extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock-capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size. With this term present, we prove a maximum norm bound for finite element solutionsof Burgers' equation an thus complete an earlier convergence proof for this equation. We further prove, using entropy variables, that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables. Results of some numerical experiments for the time-dependent compressible Euler equations in two dimensions are also reported.
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