Finite element convergence analysis for the thermoviscoelastic Joule heating problem
Provides rigorous convergence analysis for a multiphysics problem relevant to thermistor applications, but the method is standard and the contribution is incremental.
The authors prove optimal convergence orders (second-order in space, first-order in time) for a finite element discretization of the thermoviscoelastic Joule heating problem, verified by numerical experiments in 2D and 3D.
We consider a system of equations that model the temperature, electric potential and deformation of a thermoviscoelastic body. A typical application is a thermistor; an electrical component that can be used e.g. as a surge protector, temperature sensor or for very precise positioning. We introduce a full discretization based on standard finite elements in space and a semi-implicit Euler-type method in time. For this method we prove optimal convergence orders, i.e. second-order in space and first-order in time. The theoretical results are verified by several numerical experiments in two and three dimensions.