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Implementation of an adaptive finite-element approximation of the Mumford-Shah functional. (English) Zbl 0961.65062
The authors present a numerical method for solving the Mumford-Shah problem \[ \int_\Omega|\nabla u(x)|^2 dx+ H^1(K)+ \int_\Omega|u(x)- g(x)|^2 dx\to \min_{u,K}. \] The given method is based on a finite element method and on adaptive meshes. The convergence of the method is proved and a numerical test is given.

MSC:
65K10 Numerical optimization and variational techniques
49M15 Newton-type methods
49J20 Existence theories for optimal control problems involving partial differential equations
Software:
BL2D-V2
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