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Condensed Galerkin element of degree m for first-order initial-value problem with O(h2m+2) super-convergent nodal solutions.
- Source :
-
Applied Mathematics & Mechanics . Apr2022, Vol. 43 Issue 4, p603-614. 12p. - Publication Year :
- 2022
-
Abstract
- 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(h2m+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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DEGREES of freedom
*FINITE element method
Subjects
Details
- Language :
- English
- ISSN :
- 02534827
- Volume :
- 43
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics & Mechanics
- Publication Type :
- Academic Journal
- Accession number :
- 156105383
- Full Text :
- https://doi.org/10.1007/s10483-022-2831-6