A Full Predictor-Corrector Finite Element Method for the One-Dimensional Heat Equation with Time-Dependent Singularities  

作　　者：Jake L. Nkeck Jake L. Nkeck(Department of Mathematics, University of Buea, Buea, Cameroon)

机构地区：[1]Department of Mathematics, University of Buea, Buea, Cameroon

出　　处：《Journal of Applied Mathematics and Physics》2024年第4期1364-1382,共19页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：SINGULARITIES Finite Element Methods Heat Equation Predictor-Corrector Algorithm 

分 类 号：O17[理学—数学]