Two-grid methods for nonlinear pseudo-parabolic integro-differential equations by finite element method. (English) Zbl 07894779
Summary: In this paper, two efficient two-grid finite element algorithms are proposed for solving two-dimensional nonlinear pseudo-parabolic integro-differential equations. Firstly, we obtain optimal error estimates of the fully discrete finite element method using a temporal-spatial error splitting technique in \(H^1\) and \(L^p\) norms. Then the two-grid technique to improve computation efficiency of the proposed finite element method. Error estimates in \(H^1\) and \(L^p\) norms of two-grid solutions are presented. Theoretical analysis shows that the two-grid algorithms maintain asymptotically optimal accuracy. Finally, numerical examples are provided to support our theoretical results and demonstrate the effectiveness of these methods.
Keywords:
pseudo-parabolic integro-differential equations; finite element method; two-grid algorithm; error estimateReferences:
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