%0 Journal Article
%T A Full Predictor-Corrector Finite Element Method for the One-Dimensional Heat Equation with Time-Dependent Singularities
%A Jake L. Nkeck
%J Journal of Applied Mathematics and Physics
%P 1364-1382
%@ 2327-4379
%D 2024
%I Scientific Research Publishing
%R 10.4236/jamp.2024.124084
%X 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.
%K Singularities
%K Finite Element Methods
%K Heat Equation
%K Predictor-Corrector Algorithm
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=132888