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Renardy, M. and Rogers, R. (2004) An Introduction to Artial Differential Equations. 2nd Edition, Springer-Verlag, New York.

has been cited by the following article:

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

  AUTHORS: Jake L. Nkeck

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.4, April 30, 2024

  ABSTRACT: 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.