Premium
A conservative finite element method for heat conduction problems
Author(s) -
Banaszek Jerzy
Publication year - 1984
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.1620201107
Subject(s) - finite element method , galerkin method , discretization , mathematics , interpolation (computer graphics) , piecewise , mathematical optimization , a priori and a posteriori , orthogonalization , mixed finite element method , stability (learning theory) , mathematical analysis , algorithm , computer science , engineering , animation , philosophy , computer graphics (images) , machine learning , structural engineering , epistemology
This paper is concerned with the development of a numerical model which is based on the direct integral balance of internal energy over an a priori defined subdomain, associated with any nodal point, and on the piecewise temperature and geometrical interpolation inherent in the isoparametric finite element concept. This discretization procedure, also called the conservative finite element method (CFEM), ensures local and global energy conservation, in spite of discretization errors, and preserves the major feature of the finite element technique, i.e. the versatility of its algorithm. The CFEM equations are first developed and then some features of the CFEM matrices and solutions are compared with relevant features of the finite element method based on the Galerkin orthogonalization process (GFEM). To confirm better accuracy of the numerical procedure thus developed, four examples of a comparative nature, dealing with simple configurations, are solved. Furthermore, the stability and oscillation characteristics of the CFEM and GFEM solutions are established by means of the von Neumann approach, in order to show less stringent stability requirements for the CFEM model.