康彤 等 (2020):Numerical Methods for Partial Differential Equations

  • 邓钰宏
  • 创建于 2020-11-03

文章标题:Fully discrete Tψ finite element method to solve a nonlinear induction hardening problem

 

文章摘要:We study an induction hardening model described by Maxwell's equations coupled with a heat equation. The magnetic induction field is assumed a nonlinear constitutional relation and the electric conductivity is temperaturedependent. The Tψ method is to transform Maxwell's equations to the vector–scalar potential formulations and to solve the potentials by means of the finite element method. In this article, we present a fully discrete Tψ finite element scheme for this nonlinear coupled problem and discuss its solvability. We prove that the discrete solution converges to a weak solution of the continuous problem. Finally, we conclude with two numerical experiments for the coupled system.

 

引用信息:Kang T., Wang R., Zhang H., (2020). Fully discrete Tψ finite element method to solve a nonlinear induction hardening problem. Numerical Methods for Partial Differential Equations, doi.org/10.1002/num.22540.