Stable Approximations of a Minimal Surface Problem with Variational Inequalities

M. Zuhair Nashed and Otmar Scherzer

Abstract and Applied Analysis, 1997, vol. 2, 1-25

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 B V ( Ω ) of functions of bounded variation. The problem can be reformulated as an unconstrained minimization problem of a functional 𝒥 on B V ( Ω ) defined by 𝒥 ( u ) = 𝒜 ( u ) + ∫ ∂ Ω | T u − Φ | , where 𝒜 ( u ) is the “area integral” of u with respect to Ω , T is the “trace operator” from B V ( 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.

Date: 1997
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2/383457.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2/383457.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:383457

DOI: 10.1155/S1085337597000316

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().