In this paper, we discuss a generalized finite element interpolation problem and obtain the asymptotic expansion of the interpolation function. Based on these results, the error asymptotic expansion and superconvergen...In this paper, we discuss a generalized finite element interpolation problem and obtain the asymptotic expansion of the interpolation function. Based on these results, the error asymptotic expansion and superconvergence result of the generalized finite element approximation are derived. Finallym using the Superconvergent Patch Recovery Technique (SPR) proposed by Zienkiewicz & Zhu, we get the superconvergent recovery approximation and the posteriori error estimates to the flux. The numerical test convinced our analysis.展开更多
In this paper, we construct the general odd degree semi-orthogonal multi-knots spline wavelets space with point value vanishing properties under energy inner product, and present two kinds of low order compactly suppo...In this paper, we construct the general odd degree semi-orthogonal multi-knots spline wavelets space with point value vanishing properties under energy inner product, and present two kinds of low order compactly supported spline wavelets. Then we get the inheritive fast adaptive spline interpolation scheme and the prop- erties of singularity detecting with waveltets. As a result, the adaptive spline wavelets orthogonal collocation methods for initial boundary value problems are obtained.展开更多
This paper discuss the bicubic spline element solution for plate problem, we obtain the superconvergence result with two order higher than ordinary accuracy,i.e.Moreover, we get the asympototic expansion and superconv...This paper discuss the bicubic spline element solution for plate problem, we obtain the superconvergence result with two order higher than ordinary accuracy,i.e.Moreover, we get the asympototic expansion and superconvergence result of the first and second derivatives. A combination formula of the second derivative which have the accuracy of O(h4) is also derived.展开更多
文摘In this paper, we discuss a generalized finite element interpolation problem and obtain the asymptotic expansion of the interpolation function. Based on these results, the error asymptotic expansion and superconvergence result of the generalized finite element approximation are derived. Finallym using the Superconvergent Patch Recovery Technique (SPR) proposed by Zienkiewicz & Zhu, we get the superconvergent recovery approximation and the posteriori error estimates to the flux. The numerical test convinced our analysis.
文摘In this paper, we construct the general odd degree semi-orthogonal multi-knots spline wavelets space with point value vanishing properties under energy inner product, and present two kinds of low order compactly supported spline wavelets. Then we get the inheritive fast adaptive spline interpolation scheme and the prop- erties of singularity detecting with waveltets. As a result, the adaptive spline wavelets orthogonal collocation methods for initial boundary value problems are obtained.
文摘This paper discuss the bicubic spline element solution for plate problem, we obtain the superconvergence result with two order higher than ordinary accuracy,i.e.Moreover, we get the asympototic expansion and superconvergence result of the first and second derivatives. A combination formula of the second derivative which have the accuracy of O(h4) is also derived.
