Approximation of minimal surfaces with free boundaries: convergence results
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Abstract In a previous paper we developed a penalty method to approximate solutions of the free boundary problem for minimal surfaces by solutions of certain variational problems depending on a parameter $\lambda $. There we showed existence and $C^2$-regularity of these solutions as well as convergence to the solution of the free boundary problem for $\lambda \to \infty $. In this paper we develop a fully discrete finite element procedure for approximating solutions of these variational problems and prove a convergence estimate, which includes an order of convergence with respect to the grid size.
1992 ◽
pp. 221-302
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2015 ◽
Vol 29
(3)
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pp. 957-979
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2016 ◽
Vol 09
(06)
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pp. 1650080
2018 ◽
Vol 35
(4)
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pp. 993-1017
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2016 ◽
Vol 23
(1)
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pp. 195-215
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1972 ◽
Vol 330
(1583)
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pp. 573-580
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