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 degre...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.展开更多
Presents a study which proposed a dual approximate expression of the exact solution for mixed boundary value problems of second order elliptic partial differential equation with small periodic coefficients. Dual appro...Presents a study which proposed a dual approximate expression of the exact solution for mixed boundary value problems of second order elliptic partial differential equation with small periodic coefficients. Dual approximate error estimates; Main results.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.51878383 and51378293)。
文摘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.
基金the National Natural Science Foundation of China under grants 19901014 and 19932030 and the GAS K.C.Wong Poet-doctoral Resear
文摘Presents a study which proposed a dual approximate expression of the exact solution for mixed boundary value problems of second order elliptic partial differential equation with small periodic coefficients. Dual approximate error estimates; Main results.
