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Convergence of free boundaries in discrete obstacle problems

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Abstract

We show that a piecewise linear finite element approximation of the obstacle problem gives an approximate free boundary converges, in an appropriate distance, to the free boundary of the continuous problem under a stability condition on the obstacle.

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  1. Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY, 11794, USA

    Yongmin Zhang

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  1. Yongmin Zhang
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Correspondence to Yongmin Zhang.

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Zhang, Y. Convergence of free boundaries in discrete obstacle problems. Numer. Math. 106, 157–164 (2007). https://doi.org/10.1007/s00211-006-0052-z

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  • DOI: https://doi.org/10.1007/s00211-006-0052-z

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