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Error estimates for a class of discontinuous Galerkin methods for nonsmooth problems via convex duality relations (2004.09196v1)
Published 20 Apr 2020 in math.NA and cs.NA
Abstract: We devise and analyze a class of interior penalty discontinuous Galerkin methods for nonlinear and nonsmooth variational problems. Discrete duality relations are derived that lead to optimal error estimates in the case of total-variation regularized minimization or obstacle problems. The analysis provides explicit estimates that precisely determine the role of stabilization parameters. Numerical experiments suppport the optimality of the estimates.