Linear tetrahedral finite elements for thermal shock problems

Abstract

The thermal analysis using linear standard tetrahedral finite elements may be affected by spurious local extrema in the regions affected by thermal shocks, in such a severe way to directly discourage the use of these elements. The present work proposes a slight modification to the discrete heat equation in order to obtain a system matrix in M-matrix form, which assures an oscillation-free solution. The performance of this method is evaluated by means of test case with analytical solution, as well as an industrial application, for which a well-behaved numerical solution is available