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 Si YUAN;Quan YUAN

作者机构：Department of Civil EngineeringKey Laboratory of Civil Engineering Safety and Durability of China Education MinistryTsinghua UniversityBeijing 100084China 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2022年第43卷第4期

页      面：603-614页

核心收录：

学科分类：07[理学] 08[工学] 070102[理学-计算数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

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

主　　题：Galerkin method finite element method(FEM) condensed element superconvergence adjoint operator initial-value problem(IVP) 

摘      要：A new type of Galerkin finite element for first-order initial-value problems(IVPs)is *** the trial and test functions employ the same m-degreed *** 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 *** 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+*** 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.