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A Multigrid Algorithm for a Robust Finite Element Method for Solving Darcy-Stokes Problems

Author: WangMei
Tutor: ChenJinRu
School: Nanjing Normal University
Course: Computational Mathematics
Keywords: Darcy-Stokes Problem Multigrid Methods Robust Finite Element
CLC: O241.82
Type: Master's thesis
Year: 2013
Downloads: 9
Quote: 0
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Abstract


This paper proposes a multigrid algorithm for a robust finite element method which is introduced in [20] for solving Darcy-Stokes problems.In this paper, we first introduce the variational form and the corresponding dis-crete form of the Darcy-Stokes problem, and define the corresponding norm, space, and operators. Next, we present the grid transfer operator and present our multigrid algorithm. Based on a series of lemmas and theorems, we prove the smoothness and the approximation, and obtain the convergence of multigrid algorithm. We prove that under the||·||0and||·||ι2norms the error is inverse proportional to smooth frequen-cies. Therefore, when we continue to increase times of smoothness, reasonaly, under the||·||o and||·||ι2norms the error can approach zero. Finally, numerical experiments are presented to confirm our theoretical results.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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