A Semismooth Newton Solver and its application to an $hp$-FE Discretization in Elastoplasticity
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917096950071296 |
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| author | Bammer, Patrick Banz, Lothar Schönauer, Miriam Schröder, Andreas |
| author_facet | Bammer, Patrick Banz, Lothar Schönauer, Miriam Schröder, Andreas |
| contents | 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 $p$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_17295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Semismooth Newton Solver and its application to an $hp$-FE Discretization in Elastoplasticity Bammer, Patrick Banz, Lothar Schönauer, Miriam Schröder, Andreas Numerical Analysis 65H10, 65N30 G.1.5; G.1.8 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 $p$. |
| title | A Semismooth Newton Solver and its application to an $hp$-FE Discretization in Elastoplasticity |
| topic | Numerical Analysis 65H10, 65N30 G.1.5; G.1.8 |
| url | https://arxiv.org/abs/2511.17295 |