Using DUNE-ACFem for Non-smooth Minimization of Bounded Variation Functions

Martin Alkämper, Andreas Langer

Abstract


The utility of Dune-ACFem is demonstrated to work well for solving a non-smooth
minimization problem over bounded variation functions by implementing a primal-dual algo-
rithm. The implementation is based on the simplification provided by Dune-ACFem. Moreover,
the convergence of the discrete minimizer to the continuous one is shown theoretically.


Keywords


Finite Elements; DUNE; Total Variation Minimization; Denoising; Mixed Noise; Image Reconstruction

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DOI: https://doi.org/10.11588/ans.2017.1.27475

URN (PDF): http://nbn-resolving.de/urn:nbn:de:bsz:16-ans-274751