On very accurate verification of solutions for boundary value problems by using spectral methods

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概要

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• In this paper, we consider a numerical verification method of solutions for nonlinear elliptic boundary value problems with very high accuracy. We derive a constructive error estimates for the $H^1_0$-projection into polynomial spaces by using the property of the Legendre polynomials. On the other hand, the Galerkin approximation with higher degree polynomials enables us to get very small residual errors. Combining these results with existing verification procedures, several verification examples which confirm us the actual effectiveness of the method are presented.

• The Japan Society for Industrial and Applied Mathematicsの論文

著者

• Nakao Mitsuhiro

  Faculty Of Mathematics Kyushu University

• Kinoshita Takehiko

  Graduate School of Mathematics, Kyushu University

関連論文

• Numerical Verification Method of Solutions for Elliptic Equations and Its Application to the Rayleigh-Benard Problem
• On very accurate verification of solutions for boundary value problems by using spectral methods

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