Condensed Galerkin element of degree m for first-order initial-value problem with O(h^(2m+2))super-convergent nodal solutions
Condensed Galerkin element of degree m for first-order initial-value problem with O(h2m+2) super-convergent nodal solutions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.