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SUPERCONVERGENCE AND EXTRAPOLATION OF QUASI-WILSON NONCONFORMING ELEMENT METHOD FOR HYPERBOLIC INTEGRO-DIFFERENTIAL EQUATION

Shi Yanhua, Dongyang Shi

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Abstract

In this paper,the nonconforming quasi-Wilson element method is applied to approximate the hyperbolic integro-differential equation with semi-discrete scheme.This element has a special character that the consistency error can reach to order O(h~2)/O(h~3) in broken H~1-norm(one/two order higher than its interpolaion error) when exact solution u belongs to H~3(Ω)/H~4(Ω).Thus,the superclose property and global superconvergence result with order O(h~2)are obtained by combining the known high accuracy analysis of bilinear element and post-processing technique,which are the same as that of bilinear element in the existing literatures.Furthermore,the accuracy of extrapolation solution with third order is presented by constructing a new extrapolation scheme.

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What this paper is about

In this paper,the nonconforming quasi-Wilson element method is applied to approximate the hyperbolic integro-differential equation with semi-discrete scheme.This element has a special character that the consistency error can reach to order O(h~2)/O(h~3) in broken H~1-norm(one/two order higher than its interpolaion error) when exact solution u belongs to H~3(Ω)/H~4(Ω).Thus,the superclose property and global superconvergence result with order O(h~2)are obtained by combining the known high accuracy analysis of bilinear element and post-processing technique,which are the same as that of bilinear element in the existing literatures.Furthermore,the accuracy of extrapolation solution with third order is presented by constructing a new extrapolation scheme.

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Available abstract

In this paper,the nonconforming quasi-Wilson element method is applied to approximate the hyperbolic integro-differential equation with semi-discrete scheme.This element has a special character that the consistency error can reach to order O(h~2)/O(h~3) in broken H~1-norm(one/two order higher than its interpolaion error) when exact solution u belongs to H~3(Ω)/H~4(Ω).Thus,the superclose property and global superconvergence result with order O(h~2)are obtained by combining the known high accuracy analysis of bilinear element and post-processing technique,which are the same as that of bilinear element in the existing literatures.Furthermore,the accuracy of extrapolation solution with third order is presented by constructing a new extrapolation scheme.

Key concepts: Superconvergence, Extrapolation, Bilinear interpolation, Mathematics, Element (criminal law), Hyperbolic partial differential equation, Norm (philosophy), Consistency (knowledge bases)

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SUPERCONVERGENCE AND EXTRAPOLATION OF QUASI-WILSON NONCONFORMING ELEMENT METHOD FOR HYPERBOLIC INTEGRO-DIFFERENTIAL EQUATION — Research Paper | ScholarLens