Volume 55, Number 4, July-August 2021
|Page(s)||1347 - 1374|
|Published online||07 July 2021|
A priori error estimates for the space-time finite element approximation of a quasilinear gradient enhanced damage model
Faculty of Mathematics, University of Duisburg-Essen, 45127 Essen, Germany
* Corresponding author: email@example.com
Accepted: 26 April 2021
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a quasilinear gradient enhanced damage model. The model equations are of a special structure as the state equation consists of two quasilinear elliptic PDEs which have to be fulfilled at almost all times coupled with a nonsmooth, semilinear ODE that has to hold true in almost all points in space. The system is discretized by a constant discontinuous Galerkin method in time and usual conforming linear finite elements in space. Numerical experiments are added to illustrate the proven rates of convergence.
Mathematics Subject Classification: 65J08 / 65M12 / 65M15 / 65M60
Key words: Error estimates / finite elements / quasilinear coupled PDE-ODE system / damage material model
© The authors. Published by EDP Sciences, SMAI 2021
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