Superconvergence for triangular cubic elements  

作　　者：Chuanmiao Chen Jicheng Jin Shi Shu 

机构地区：[1]Hunan Normal Univ, Inst Comp, Changsha 410081, Peoples R China [2]Xiangtan Univ, Dept Math, Xiangtan 411105, Peoples R China

出　　处：《Chinese Science Bulletin》1999年第1期47-49,共3页

摘　　要：A new structure of superconvergence for the cubic triangular finite element approximation u/2 to a second-order elliptic problem Au=f is studied based on some orthogonal expansions in an interval. Suppose that Ω is a convex polygonal domain with boundary L, its triangulation is uniform and T_h is a set of vertexes and side midpoints of all elements. Then u_h itself has no superconvergence points in Ω, while in any interior subdomain Ω₀ the average gradient Du_h has superconvergence D（d_h-u）=O(h^m+1lnh) at z∈T_h∩Ω₀（no other superconvergence points）. Furthermore, prescribe u=0 on L₁.Then the superconvergence near L₁ will surely disappear; if αa_vu+bu=0 on L₃, where v is the conormal direction, the numercal experiments show superconvergence up to L₃（the case of A=-Δ and b=0 has already been proved）.A new structure of superconvergence for the cubic triangular finite element approximationu/2 to a second-order elliptic problemAu = f is studied based on some orthogonal expansions in an interval. Suppose that Ω is a convex polygonal domain with boundary Γ, its triangulation is uniform andT h is a set of vertexes and side midpoints of all elements. Thenu h itself has no superconvergence points in Ω, while in any interior subdomain Ω0 the average gradientDu h has superconvergenceD(d h ?u) = O(h m+1 Inh) at z ∈T h ∩ Ω0(no other superconvergence points). Furthermore, prescribeu = 0 on Γ1. Then the superconvergence near Γ1 will surely disappear; ifa?u + bu = 0 on Γ3, where ν is the conormal direction, the numercal experiments show superconvergence up to Γ3(the case ofA = ? Δ andb = 0 has already been proved).

关 键 词：SUPERCONVERGENCE TRIANGULAR CUBIC ELEMENT FINITE ELEMENT approxination. 

分 类 号：O241[理学—计算数学]