Finite element approximation of a nonlinear heat conduction problem in anisotropic media

• Date: 6. 10. 2022
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Michal Křížek

We will survey results which we have obtained in solving a stationary nonlinear heat conduction problem by the finite element method. In particular, we present uniqueness theorems for the classical and weak solutions, a comparison principle, existence theorems for the weak and finite element solutions, convergence of finite element approximations and a priori error estimates. Further, we introduce some superconvergence phenomena by a suitable post-processing operator and nonlinear radiation boundary conditions. Finally, we illustrate how to apply the obtained theoretical results for solving several real-life technical problems.