Numerical Simulation of 4th Order Total Variation Flow Problem by using C^0 IPDG Method
Bhandari, Chandi Prasad 1985-
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This dissertation is devoted to the the numerical solution of the regularized fourth order total variation flow problem in material science representing surface relaxation below the roughening temperature. Based on regularization and a scaling in time and space, the problem is discretized implicitly in time by the backward Euler scheme and discretized in space by C$^0$ Interior Penalty Discontinuous Galerkin (C$^0$IPDG) method. In particular, it is showed that at each time instant the C$^0$IPDG approximation represents the necessary and sufficient optimality condition for the minimization of an associated proper convex, coercive, and lower semi-continuous objective functional. The main results are a priori error estimates of the global discretization error in a mesh dependent C$^0$IPDG-norm and the L$^2$-norm. A documentation of numerical results is provided illustrating the performance of the C$^0$IPDG method and predictor corrector continuation strategies.