Finite Element Convergence for the Joule Heating Problem with Mixed Boundary Conditions

Details Finite Element Convergence for the Joule Heating Problem with Mixed Boundary Conditions Finite Element Convergence for the Joule Heating Problem with Mixed Boundary Conditions

2012-03-28

arxiv.org/abs/1203.6306v1

Mathematics

Numerical Analysis

Keywords: Joule heating problem, thermistors, a posteriori error analysis, a priori error analysis, finite element method

Scientific paper

We prove strong convergence of conforming finite element approximations to
the stationary Joule heating problem with mixed boundary conditions on
Lipschitz domains in three spatial dimensions. We show optimal global
regularity estimates on creased domains and prove a priori and a posteriori
bounds for shape regular meshes.

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