Discontinuous Galerkin time discretization in elastoplasticity: motivation, numerical algorithms, and applications

Abstract

Discontinuous Galerkin discretizations promise to become a very flexible tool in hp-adaptive space–time discretizations. This is very attractive for moving interphase problems such as the free boundary between the elastic and plastic phase in elastoplastic time evolution. The mathematical model of which involves variational inequalities and so the distributional time derivative is not obviously generalized to discontinuous test functions. This paper motivates and introduces a discontinuous Galerkin (dG) time discretization. Solution algorithms and examples are established which support feasibility and accuracy of the proposed schemes dG(0) and dG(1). The methods are compared with a backward Euler and Crank–Nicholson scheme.