Publication 18-CNA-006
A penalty method for some nonlinear variational obstacle problems
Hayden Schaeffer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
schaeffer@cmu.edu
Abstract: We formulate a penalty method for the obstacle problem
associated with a nonlinear variational principle. It is proven that the
solution to the relaxed variational problem (in both the continuous and
discrete settings) is exact for finite parameter values above some
calculable quantity. To solve the relaxed variational problem, an
accelerated forward-backward method is used, which ensures convergence
of the iterates, even when the Euler-Lagrange equation is degenerate and
non-differentiable. Several nonlinear examples are presented, including
quasi-linear equations, degenerate and singular elliptic operators,
discontinuous obstacles, and a nonlinear two-phase membrane problem.
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