Error estimates of spectral Legendre–Galerkin methods for the fourth-order equation in one dimension

Yanping Chen and Jianwei Zhou

Applied Mathematics and Computation, 2015, vol. 268, issue C, 1217-1226

Abstract: We employ spectral Legendre–Galerkin and mixed Legendre–Galerkin approximations to solve the first bi-harmonic equation in one dimension, respectively. By orthogonal properties of Legendre polynomials, we obtain an explicit a posteriori error indicator for spectral Legendre–Galerkin methods. Furthermore, in virtue of an auxiliary variable, we present spectral mixed Legendre–Galerkin methods and study the a priori estimate and a posteriori error indicator. Especially, these indicators only depend on the expansions of the right-hand item. Numerical examples are presented to verify our theoretical analysis.

Keywords: A posteriori error indicator; A priori error estimate; Spectral Galerkin method; Legendre polynomial (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:1217-1226

DOI: 10.1016/j.amc.2015.06.082

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