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arXiv · 1710.00529

Nonlinear discontinuous Petrov-Galerkin methods

Carsten Carstensen·Philipp Bringmann·Friederike Hellwig·Peter Wriggers
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Abstract

The discontinuous Petrov-Galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper. Its lowest-order version applies to a nonlinear uniformly convex model example and is equivalently characterized as a mixed formulation, a reduced formulation, and a weighted nonlinear least-squares method. Quasi-optimal a priori and reliable and efficient a posteriori estimates are obtained for the abstract nonlinear dPG framework for the approximation of a regular solution. The variational model example allows for a built-in guaranteed error control despite inexact solve. The subtle uniqueness of discrete minimizers is monitored in numerical examples.

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Carsten Carstensen, Philipp Bringmann, Friederike Hellwig, Peter Wriggers. 2017-10-02. Nonlinear discontinuous Petrov-Galerkin methods. https://arxiv.org/abs/1710.00529

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