A derivative patch interpolating recovery technique is analyzed for the finite element approximation to the second order elliptic boundary value problems in two dimensional case.It is shown that the convergence rate o...A derivative patch interpolating recovery technique is analyzed for the finite element approximation to the second order elliptic boundary value problems in two dimensional case.It is shown that the convergence rate of the recovered gradient admits superc onvergence on the recovered subdomain, and is two order higher than the optimal global convergence rate (ultracovergence) at an internal node point when even order finite element spaces and local uniform meshes are used.展开更多
In this paper, the linear finite element approximation to the positive and symmetric,linear hyperbolic systems is analyzed and an O(h^2) order error estimate is established under the conditions of strongly regular tri...In this paper, the linear finite element approximation to the positive and symmetric,linear hyperbolic systems is analyzed and an O(h^2) order error estimate is established under the conditions of strongly regular triangulation and the H^3-regularity for the exact solutions. The convergence analysis is based on some superclose estimates derived in this paper. Our method and result here are also applicable to general hyperbolic problems.Finally, we discuss the linearized shallow water system of equations.展开更多
文摘A derivative patch interpolating recovery technique is analyzed for the finite element approximation to the second order elliptic boundary value problems in two dimensional case.It is shown that the convergence rate of the recovered gradient admits superc onvergence on the recovered subdomain, and is two order higher than the optimal global convergence rate (ultracovergence) at an internal node point when even order finite element spaces and local uniform meshes are used.
文摘In this paper, the linear finite element approximation to the positive and symmetric,linear hyperbolic systems is analyzed and an O(h^2) order error estimate is established under the conditions of strongly regular triangulation and the H^3-regularity for the exact solutions. The convergence analysis is based on some superclose estimates derived in this paper. Our method and result here are also applicable to general hyperbolic problems.Finally, we discuss the linearized shallow water system of equations.
