- CARMA SEMINAR
- Speaker: Ernst Stephan, Insitut fur Angewandte Mathematik (IfAM), Leibniz Universitat Hannover
- Title: hp-adaptive DG-FEM for Parabolic Obstacle Problems
- Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 3:00 pm, Tue, 13th Mar 2012
Parabolic obstacle problems find applications in the financial markets for pricing American put options. We present a mixed and an equivalent variational inequality hp-interior penalty DG (IPDG) method combined with an hp-time DG (TDG) method to solve parabolic obstacle problems approximatively. The contact conditions are resolved by a biorthogonal Lagrange multiplier and are component-wise decoupled. These decoupled contact conditions are equivlent to finding the root of a non-linear complementary function. This non-linear problem can in turn be solved efficiently by a semi-smooth Newton method. For the hp-adaptivity a p-hierarchical error estimator in conjunction with a local analyticity estimate is employed. For the considered stationary problem, this leads to exponential convergence, and for the instationary problem to greatly improved convergence rates. Numerical experiments are given demonstrating the strengths and limitations of the approaches.
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