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2013•Journal of Henan Normal UniversityRequires access

Superconvergence Analysis of Quasi-Wilson Element for Nonlinear Hyperbolic Equation

Wang Fenlin

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Abstract

Nonconforming quasi-Wilson finite element approximation to nonlinear hyperbolic equation is discussed for the semi-discrete scheme.By use of the special property of the element,i.e.,the consistence error in energy norm is of order O(h2),one order higher than its interpolation error,the superclose property with order O(h2)is derived by higher accuracy analysis of its conforming part,the derivative transfering and mean-value technique.Furthermore,the superconvergence result is obtained through the interpolated postprocessing method.

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What this paper is about

Nonconforming quasi-Wilson finite element approximation to nonlinear hyperbolic equation is discussed for the semi-discrete scheme.By use of the special property of the element,i.e.,the consistence error in energy norm is of order O(h2),one order higher than its interpolation error,the superclose property with order O(h2)is derived by higher accuracy analysis of its conforming part,the derivative transfering and mean-value technique.Furthermore,the superconvergence result is obtained through the interpolated postprocessing method.

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Available abstract

Nonconforming quasi-Wilson finite element approximation to nonlinear hyperbolic equation is discussed for the semi-discrete scheme.By use of the special property of the element,i.e.,the consistence error in energy norm is of order O(h2),one order higher than its interpolation error,the superclose property with order O(h2)is derived by higher accuracy analysis of its conforming part,the derivative transfering and mean-value technique.Furthermore,the superconvergence result is obtained through the interpolated postprocessing method.

Key concepts: Superconvergence, Mathematics, Nonlinear system, Norm (philosophy), Interpolation (computer graphics), Hyperbolic partial differential equation, Finite element method, Element (criminal law)

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