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

Bartels, Sören

doi:10.1090/mcom/3656

Error estimates for a class of discontinuous Galerkin methods for nonsmooth problems via convex duality relations
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Math. Comp. 90 (2021), 2579-2602 Request permission

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 confirm the optimality of the estimates.

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