Convergence of \(\mathrm{dG}(1)\) in elastoplastic evolution
The discontinuous Galerkin time discretization, abbreviated as dG(\(k\)), with a polynomial degree at most \(k\in \mathbb{N}_0\) of elastoplastic evolution problems is discussed. The paper has the following structure. Section 1 is an introduction and overview. Section 2 is devoted to the strong form of a model example in elastoplasticity with hardening and the weak primal and dual form. The resulting fully discrete scheme is a variational inequality at each time-step and it is given in Section 3. The equivalence of two discrete formulations, the dual and the primal one, is given in this section. The error analysis in Section 4 explains and verifies the asymptotic convergence result. In Section 5, the numerical investigation for a benchmark problem with known analytic solution provides empirical evidence of a higher convergence rate of the dG(1) scheme compared to dG(0).
scientific article; zbMATH DE number 7027402