Condensed Galerkin element of degree m for first-order initial-value problem with O(h^(2m+2))super-convergent nodal solutions  

作　　者：Si YUAN Quan YUAN 

机构地区：[1]Department of Civil Engineering,Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry,Tsinghua University,Beijing 100084,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2022年第4期603-614,共12页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.51878383 and51378293)。

摘　　要：A new type of Galerkin finite element for first-order initial-value problems(IVPs)is proposed.Both the trial and test functions employ the same m-degreed polynomials.The adjoint equation is used to eliminate one degree of freedom(DOF)from the test function,and then the so-called condensed test function and its consequent condensed Galerkin element are constructed.It is mathematically proved and numerically verified that the condensed element produces the super-convergent nodal solutions of O(h^(2m+2)),which is equivalent to the order of accuracy by the conventional element of degree m+1.Some related properties are addressed,and typical numerical examples of both linear and nonlinear IVPs of both a single equation and a system of equations are presented to show the validity and effectiveness of the proposed element.

关 键 词：Galerkin method finite element method(FEM) condensed element SUPERCONVERGENCE adjoint operator initial-value problem(IVP) 

分 类 号：O242.21[理学—计算数学] O302[理学—数学]