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Item type:Publication, Access status: with files , Numerical solution of nonlinear finite element problems in elasticity(2026); We consider high-order finite element discretizations of displacement problems on elastic bodies under external loading. In general, the deformation of an elastic body is nonlinear with respect to the applied load. Divergence of the nonlinear solver is prevented by applying the loads in increments. We study a modification of the traditional incremental load step method that exploits the hierarchical finite element discretization. We test the new approach on a benchmark problem in computational mechanics and on a displacement-driven foam pore problem.Publicationtype: Doctoral Thesis65 61 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Using surrogate models to accelerate load step methods for nonlinear finite element problems in hyperelasticityFinite element methods for displacement problems in hyperelasticity lead to systems of nonlinear equations. These equations are usually solved with Newton's method or a related method. The convergence of Newton's method depends heavily on the proximity of the initial guess to the numerical solution. Load step methods overcome problems with divergence by applying the load in increments, leading to a sequence of sub‐problems with initial guesses closer to the numerical solution of each sub‐problem, supporting the convergence. The downside of this approach is the high computational effort needed to solve the load steps. Based on a benchmark problem in high‐order FEM, we extend traditional load step methods to a new approach exploiting the hierarchical basis used for the spatial discretization of the problem and saving up to 50% of computation time (vs. benchmark).Publicationtype: Journal Article38 33