Geodesic
Approximation of minimal surfaces with free boundaries
Ulrich Dierkes1 orcid ; Tristan Jenschke1 ; Paola Pozzi1
1Universität Duisburg-Essen, Germany
Interfaces and free boundaries, Tome 20 (2018) no. 4, pp. 551-576

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DOI

In this paper we develop a penalty method to approximate solutions of the free boundary problem for minimal surfaces. To this end we study the problem of finding minimizers of a functional Fλ​ which is defined as the sum of the Dirichlet integral and an appropriate penalty term weighted by a parameter λ. We prove existence of a solution for λ large enough as well as convergence to a solution of the free boundary problem as λ tends to infinity. Additionally regularity at the boundary of these solutions is shown, which is crucial for deriving numerical error estimates. Since every solution is harmonic, the analysis is largely simplified by considering boundary values only and using harmonic extensions.
DOI : 10.4171/ifb/412
Classification : 53-XX, 49-XX, 65-XX
Mots-clés : Minimal surfaces, free boundary problem, finite element approximation, convergence

Ulrich Dierkes  1   ; Tristan Jenschke  1   ; Paola Pozzi  1

1 Universität Duisburg-Essen, Germany 
Ulrich Dierkes; Tristan Jenschke; Paola Pozzi. Approximation of minimal surfaces with free boundaries. Interfaces and free boundaries, Tome 20 (2018) no. 4, pp. 551-576. doi: 10.4171/ifb/412
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     pages = {551--576},
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     doi = {10.4171/ifb/412},
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