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arXiv · 2511.17295

A Semismooth Newton Solver and its application to an $hp$-FE Discretization in Elastoplasticity

Patrick Bammer·Lothar Banz·Miriam Schönauer·Andreas Schröder
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Abstract

In this paper, we consider a class of systems of nonlinear equations, which arise in discretized mixed formulations of problems in solid mechanics by $hp$-finite elements. We introduce a semismooth Newton solver for this specific class and prove its well-definedness and local convergence. Thereby, the analysis heavily relies on a special eigenvalue interplay of two matrices involved in the considered nonlinear system. Next, we apply the general results to an $hp$-finite element discretization of a problem in elastoplasticity, which can be formulated as a system of nonlinear equations of the above type by using biorthogonal basis functions. Finally, numerical examples demonstrate the applicability and robustness of the proposed semismooth Newton solver with respect to $h$ and $p$.

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Patrick Bammer, Lothar Banz, Miriam Schönauer, Andreas Schröder. 2025-11-21. A Semismooth Newton Solver and its application to an $hp$-FE Discretization in Elastoplasticity. https://arxiv.org/abs/2511.17295

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