Long-time behavior of the two-grid finite element method for fully discrete semilinear evolution equations with positive memory

• Autores: Wansheng Wang
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 250, Nº 1, 2013, págs. 161-174
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.03.006
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• Resumen

  • Based on two-grid discretizations, two fully discrete finite element algorithms for semilinear parabolic integro-differential equations with positive memory are proposed.

    With the backward Euler scheme for the temporal discretization, the basic idea of the space two-grid finite element algorithms is to approximate the semilinear equations on a coarse space grid and to solve the linearized equations on a finer space grid at each time step.

    To further decreases the amount of computational work, a space�time two-grid algorithm based on a coarse space grid with large time stepsize ÄT and a finer space grid with small time stepsize Ät for the evolutional equations is proposed in this paper. The sharp long-time stability and error estimates for the standard finite element method, the space two-grid finite element method, and the space�time two-grid finite element method are derived. It is showed that the two-grid algorithms� long-time stability and error estimates are similar to those of the direct resolution of the semilinear problem on a fine grid.