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Paper detail

Error estimates for a class of discontinuous Galerkin methods for nonsmooth problems via convex duality relations

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.

preprint2020arXivOpen access
Sören Bartels
math.NANumerical Analysis
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Sören Bartels

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