2025/11/21 by Bammer, Patrick, Banz, Lothar, Schönauer, Miriam +1
#65H10 #65N30 #FOS: Mathematics #G.1.5 #G.1.8 #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2511.17295
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.