Multigrid Methods for Elliptic Obstacle Problems on 2D Bisection Grids

Chen, Long; Nochetto, Ricardo H.; Zhang, Chen-Song

doi:10.1007/978-3-642-11304-8_25

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The Classical Obstacle Problem1

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2015

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“…Remark 2.10 (efficient solvers). The solution U T ∈ V(T ) of problem (2.7) can be efficiently computed via monotone multigrid methods; see [9] and the references therein.…”

Section: The Classical Obstacle Problemmentioning

confidence: 99%

Convergence rates for the classical, thin and fractional elliptic obstacle problems

Nochetto

Otárola

Salgado

2015

Phil. Trans. R. Soc. A.

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One contribution of 15 to a theme issue 'Free boundary problems and related topics' . We review the finite-element approximation of the classical obstacle problem in energy and max-norms and derive error estimates for both the solution and the free boundary. On the basis of recent regularity results, we present an optimal error analysis for the thin obstacle problem. Finally, we discuss the localization of the obstacle problem for the fractional Laplacian and prove quasi-optimal convergence rates.

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“…Remark 2.10 (efficient solvers). The solution U T ∈ V(T ) of problem (2.7) can be efficiently computed via monotone multigrid methods; see [9] and the references therein.…”

Section: The Classical Obstacle Problemmentioning

confidence: 99%