Author(s)

Jake L. Nkeck

Department of Mathematics, University of Buea, Buea, Cameroon.

The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.

Singularities, Finite Element Methods, Heat Equation, Predictor-Corrector Algorithm

Nkeck, J. (2024) A Full Predictor-Corrector Finite Element Method for the One-Dimensional Heat Equation with Time-Dependent Singularities. Journal of Applied Mathematics and Physics, 12, 1364-1382. doi: 10.4236/jamp.2024.124084.