Summary
We describe two algorithms for the numerical solution of mixed finite element problems which arise e.a. from the discretization of the Stokes equations. For the first algorithm we transform the original problem into an equation Lp = g involving a continuous, positive definite, symmetric linear operator L. We apply a conjugate gradient algorithm to this equation. The evaluation of Lp is done approximately using a multigrid algorithm. In the second algorithm we apply the multiarid idea directly to the indefinite problem. We use Jacobi iteration for the squared system as smoothing operator. The convergence improves when using a conjugate residual algorithm. The convergence rate is measured in a mesh dependent norm. Both algorithms have convergence rates bounded away from 1 independently of the mesh-size. We present numerical results for the first algorithm. Numerical experiments for the second algorithm are in progress.
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© 1984 Springer Fachmedien Wiesbaden
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Verfürth, R. (1984). Numerical Solution of Mixed Finite Element Problems. In: Hackbusch, W. (eds) Efficient Solutions of Elliptic Systems. Notes on Numerical Fluid Mechanics, vol 10. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14169-3_10
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DOI: https://doi.org/10.1007/978-3-663-14169-3_10
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-08084-6
Online ISBN: 978-3-663-14169-3
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