88,219 research outputs found

    Gastaldi, F.

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    Analysis of finite element approximation of evolution problems in mixed form

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    This paper deals with the finite element approximation of evolution problems in mixed form. Following [D. Boffi, F. Brezzi, L. Gastaldi, Math. Comp. 69 (2000), pp.121-140], we handle separately two types of problems. A model for the first case is the heat equation in mixed form, while the time dependent Stokes problem fits within the second one. For either case, we give sufficient conditions for a good approximation in the natural functional spaces. The results are not obvious in the first situation. In this case, the well-known conditions for the well-posedness and convergence of the corresponding steady problem are not sufficient for the good approximation of the time dependent problem. This issue is demonstrated with a numerical (counter-) example and justified analytically

    Adaptive domain decomposition methods for advection dominated equations

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    We consider several adaptive methods of domain decomposition for the solution of advection-diffusion boundary value problems. Adaptivity relies on accounting for the local direction of the convective field at subdomain interfaces. A convergence analysis is carried out both at differential and numerical level, and the algorithmical aspects of these methods are considered
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