Advanced Solvers for Nonlinear Heat Conduction with Generalized Constitutive Laws

In this paper, we discuss solvers for solving the discretized nonlinear heat equation with generalized constitutive laws. The model features multi-valued graphs, and the nonlinear functions are at best semi-smooth. Their solutions have low regularity. We identify appropriate global and local nonlinear solvers and propose and evaluate a suite of accelerated iterative algorithms with additional enhancements that improve the convergence of schemes compared to those from the literature. We illustrate these solvers with numerical examples.