This paper deals with the splitting extrapolation for mixed finite element used in the approximation of the steady Stokes equation. Applying the multi variate asymptotic expansion of the error on independent grid p...This paper deals with the splitting extrapolation for mixed finite element used in the approximation of the steady Stokes equation. Applying the multi variate asymptotic expansion of the error on independent grid parameters, we can get a parallel algorithm and a global fine grid approximations with high accuracy.展开更多
The finite element solutions of elliptic eigenvalue equations are shown to have a multi-parameter asymptotic error expansion. Based on this expansion and a splitting extrapolation technique, a parallel algorithm for s...The finite element solutions of elliptic eigenvalue equations are shown to have a multi-parameter asymptotic error expansion. Based on this expansion and a splitting extrapolation technique, a parallel algorithm for solving multi-dimensional equations with high order accuracy is developed.展开更多
Taking hm as the mesh width of a curved edge Гm （m = 1, ..., d ） of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first...Taking hm as the mesh width of a curved edge Гm （m = 1, ..., d ） of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first kind of plane elasticity Dirichlet problems on curved polygons, which possess high accuracy O（h0^3） and low computing complexities. Since multivariate asymptotic expansions of approximate errors with power hi^3 （i = 1, 2, ..., d） are shown, by means of the splitting extrapolations high precision approximations and a posteriori estimate are obtained.展开更多
In this paper,the collocation methods are used to solve the boundary integral equations of the first kind on the polygon.By means of Sidi’s periodic transformation and domain decomposition,the errors are proved to po...In this paper,the collocation methods are used to solve the boundary integral equations of the first kind on the polygon.By means of Sidi’s periodic transformation and domain decomposition,the errors are proved to possess the multi-parameter asymptotic expansion at the interior point with the powers h^(3)/_(i)(i=1,...,d),which means that the approximations of higher accuracy and a posteriori estimation of the errors can be obtained by splitting extrapolations.Numerical experiments are carried out to show that the methods are very efficient.展开更多
文摘This paper deals with the splitting extrapolation for mixed finite element used in the approximation of the steady Stokes equation. Applying the multi variate asymptotic expansion of the error on independent grid parameters, we can get a parallel algorithm and a global fine grid approximations with high accuracy.
基金This research is supported by National Science Foundation of China
文摘The finite element solutions of elliptic eigenvalue equations are shown to have a multi-parameter asymptotic error expansion. Based on this expansion and a splitting extrapolation technique, a parallel algorithm for solving multi-dimensional equations with high order accuracy is developed.
基金Supported by Natioal Science Foundation of China （10171073）.
文摘Taking hm as the mesh width of a curved edge Гm （m = 1, ..., d ） of polygons and using quadrature rules for weakly singular integrals, this paper presents mechanical quadrature methods for solving BIES of the first kind of plane elasticity Dirichlet problems on curved polygons, which possess high accuracy O（h0^3） and low computing complexities. Since multivariate asymptotic expansions of approximate errors with power hi^3 （i = 1, 2, ..., d） are shown, by means of the splitting extrapolations high precision approximations and a posteriori estimate are obtained.
文摘In this paper,the collocation methods are used to solve the boundary integral equations of the first kind on the polygon.By means of Sidi’s periodic transformation and domain decomposition,the errors are proved to possess the multi-parameter asymptotic expansion at the interior point with the powers h^(3)/_(i)(i=1,...,d),which means that the approximations of higher accuracy and a posteriori estimation of the errors can be obtained by splitting extrapolations.Numerical experiments are carried out to show that the methods are very efficient.
