Abstract
This paper aims to study the Galerkin finite element method (FEM) of both the semi-discrete and the fully-discrete schemes with linear triangular element for the time-dependent Joule heating problem. Through some new estimating approaches such as the different mathematical induction assumption, the mean-value technique and the special characters of this element, the superclose and superconvergence estimates for the related variables in the H1-norm are derived under lower regularities of the solutions of the considered problem rigorously, which simply the proof process and improve the corresponding results in the existing literature. Finally, numerical results are provided to confirm the theoretical analysis.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
