In this paper we propose a unified framework to construct interface preconditioner for non-overlapping domain decomposition methods, and prove a generalresu1t to estimate condition number of preconditioned interface m...In this paper we propose a unified framework to construct interface preconditioner for non-overlapping domain decomposition methods, and prove a generalresu1t to estimate condition number of preconditioned interface matrices. Basingon this, we analyse the essence of the known interface preconditioners, and construct a kind of interface preconditioner for hybrid element domain decompositionmethods.展开更多
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 a kind of simple preconditioner for non-overlapping domain decomposition methods with Lagrangian multipliers. It will be shown that condition numbed of the preconditioned interface matrix is...In this paper we construct a kind of simple preconditioner for non-overlapping domain decomposition methods with Lagrangian multipliers. It will be shown that condition numbed of the preconditioned interface matrix is almost optimal.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
In this paper we discuss the continuous piecewise polynomial spline collocation method for a kind of integral operator equations, which include smooth kernel Fredholm equations and Volterra equations as well as Green...In this paper we discuss the continuous piecewise polynomial spline collocation method for a kind of integral operator equations, which include smooth kernel Fredholm equations and Volterra equations as well as Green’s kernel integral equations. It will be shown that the collocation solution itself may admit an ideal error expansion at the knots. Based on this expanison, the multilevel corrected global estimates can be obtained by using the "higher order interpolation" technique.展开更多
文摘In this paper we propose a unified framework to construct interface preconditioner for non-overlapping domain decomposition methods, and prove a generalresu1t to estimate condition number of preconditioned interface matrices. Basingon this, we analyse the essence of the known interface preconditioners, and construct a kind of interface preconditioner for hybrid element domain decompositionmethods.
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 a kind of simple preconditioner for non-overlapping domain decomposition methods with Lagrangian multipliers. It will be shown that condition numbed of the preconditioned interface matrix is almost optimal.
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.
文摘In this paper we discuss the continuous piecewise polynomial spline collocation method for a kind of integral operator equations, which include smooth kernel Fredholm equations and Volterra equations as well as Green’s kernel integral equations. It will be shown that the collocation solution itself may admit an ideal error expansion at the knots. Based on this expanison, the multilevel corrected global estimates can be obtained by using the "higher order interpolation" technique.
