In this work we present son-le numerical methods for solving evolutive convection-diffusion problems. In order to obtain a physically admissible solution we search for monotone and accurate methods that are also non-l...
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ISBN:
(数字)9783642196652
ISBN:
(纸本)9783642196645
In this work we present son-le numerical methods for solving evolutive convection-diffusion problems. In order to obtain a physically admissible solution we search for monotone and accurate methods that are also non-linear due to the Godunov's theorem. We will center in Fluctuation Splitting methods, [8], in particular in PSI scheme, and characteristic type methods, where a new Lagrangian method is proposed. Finally, a numerical test is presented to assess the performance of the numerical methods described in the present work.
Schwarz domain decomposition methods can be analyzed both at the continuous and discrete level. For consistent discretizations, one would naturally expect that the discretized method performs as predicted by the conti...
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ISBN:
(纸本)9783642113031
Schwarz domain decomposition methods can be analyzed both at the continuous and discrete level. For consistent discretizations, one would naturally expect that the discretized method performs as predicted by the continuous analysis. We show in this short note for two model problems that this is not always the case, and that the discretization can both increase and decrease the convergence speed predicted by the continuous analysis.
It is well accepted that the efficient solution of complex partial differential equations (PDEs) often requires methods which are adaptive in both space and time. In this paper we are interested in a class of spatiall...
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In this paper, we develop and analyze an efficient multigrid method to solve the finite element systems from elliptic obstacle problems on two dimensional adaptive meshes. Adaptive finite element methods (AFEMs) based...
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The objective of this paper is to explain the principles of the design of a coarse space in a simplified way and by pictures. The focus is on ideas rather than on a more historically complete presentation. That can be...
We consider two-level Newton-Krylov-Schwarz algorithms for blood flow in arteries, which is a computationally difficult and practically important application area [6, 8]. In particular, the similar densities of blood ...
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Recently, it has been developed an explicit a-posteriori error estimator (Ainsworth and Oden, A posterior error estimation in finite element analysis, Wiley, 2000) especially suited for fluid dynamics problems solved ...
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ISBN:
(数字)9783642196652
ISBN:
(纸本)9783642196645
Recently, it has been developed an explicit a-posteriori error estimator (Ainsworth and Oden, A posterior error estimation in finite element analysis, Wiley, 2000) especially suited for fluid dynamics problems solved with stabilized methods (Hauke et al., Variational multiscale a-posteriori error estimation for the multi-dimensional transport equation, Comput. Meth. Appl. Mech. Eng. 195, 1573-1593, 2006;Hauke et al., The multiscale approach to error estimation and adaptivity, Comput. Meth. Appl. Mech. Eng. 197, 2701-2718, 2008;Hauke et al., Multiscale Methods in computational Mechanics, vol. 55. Springer, 2010). The technology is based upon the theory that inspired stabilized methods, namely, the variational multiscale theory (Hughes, Comput. Meth. Appl. Mech. Eng. 127, 387-401, 1995;Hughes et al., Comput. Meth. Appl. Mech. Eng. 166, 3-24, 1998). The salient features of the formulation are that it can be readily implemented in existing codes, it is a very economical procedure and it yields very accurate local error estimates uniformly from the diffusive to the advective regime. In this work, the variational multiscale error estimator is applied to develop adaptive strategies for the advection-diffusion-reaction equation. The performance of two local error norms and three strategies to adapt the mesh are investigated, with emphasis on flows with boundary and interior layers.
Poincare type inequalities play a central role in the analysis of domain decomposition and multigrid methods for second-order elliptic problems. However, when the coefficient varies within a subdomain or within a coar...
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ISBN:
(纸本)9783642113031
Poincare type inequalities play a central role in the analysis of domain decomposition and multigrid methods for second-order elliptic problems. However, when the coefficient varies within a subdomain or within a coarse grid element, then standard condition number bounds for these methods may be overly pessimistic. In this short note we present new weighted Poincare type inequalities for a class of piecewise constant coefficients that lead to sharper bounds independent of any possible large contrasts in the coefficients.
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