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Analysis of two-grid method for second-order hyperbolic equation by expanded mixed finite element methods
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Analysis of two-grid method for second-order hyperbolic equation by expanded mixed finite element methods
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Journal Article
Analysis of two-grid method for second-order hyperbolic equation by expanded mixed finite element methods
2024
Overview
In this article, we present a scheme for solving two-dimensional hyperbolic equation using an expanded mixed finite element method. To solve the resulting nonlinear expanded mixed finite element system more efficiently, we propose a two-step two-grid algorithm. Numerical stability and error estimate are proved on both the coarse grid and fine grid. It is shown that the two-grid method can achieve asymptotically optimal approximation as long as the coarse grid size
and the fine grid size
satisfy
(
), where
is the degree of the approximating space for the primary variable. Numerical experiment is presented to demonstrate the accuracy and the efficiency of the proposed method.
Publisher
De Gruyter,De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
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