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Some improvements of the finite element solution for one‐dimensional problems
Author(s) -
Gatica Gabriel N.
Publication year - 1987
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620240511
Subject(s) - finite element method , norm (philosophy) , mathematics , euclidean geometry , residual , element (criminal law) , mathematical optimization , domain (mathematical analysis) , euclidean space , method of mean weighted residuals , mathematical analysis , algorithm , geometry , engineering , structural engineering , galerkin method , political science , law
New algorithms which improve the finite element solution on a fixed mesh of the domain are developed. For this, objective functions which depend on a positive parameter to be determined are proposed. These functions lead to criteria which combine in several ways the residual of the solution, the approximation in the Euclidean norm of the value of the solution at the nodes, and the approximations in the energy and H k norms. Some aspects of optimality are studied and, finally, numerical results are given.