stable approximations of a minimal surface problem with variational inequalities
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ID: 233637
1997
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Abstract
In this paper we develop a new approach for the stable approximation of a minimal surface problem associated with a relaxed Dirichlet problem in the space BV(Ω) of functions of bounded variation. The problem can be reformulated as an unconstrained minimization problem of a functional 𝒥 on BV(Ω) defined by 𝒥(u)=𝒜(u)+∫∂Ω|Tu−Φ|, where 𝒜(u) is the “area integral” of u with respect to Ω,T is the “trace operator” from BV(Ω) into L i(∂Ω), and ϕ is the prescribed data on the boundary of Ω. We establish convergence and stability of approximate regularized solutions which are solutions of a family of variational inequalities. We also prove convergence of an iterative method based on Uzawa's algorithm for implementation of our regularization procedure.
| Reference Key |
nashed1997abstractstable
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|---|---|
| Authors | ;M. Zuhair Nashed;Otmar Scherzer |
| Journal | science and technology of advanced materials |
| Year | 1997 |
| DOI |
10.1155/S1085337597000316
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