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On the accuracy of finite element solutions to the transient heat‐conduction equation
Author(s) -
Donea J.
Publication year - 1974
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.1620080109
Subject(s) - finite element method , thermal conduction , transient (computer programming) , galerkin method , mathematics , heat equation , boundary value problem , crank–nicolson method , mathematical analysis , simple (philosophy) , scheme (mathematics) , physics , computer science , thermodynamics , philosophy , epistemology , operating system
This paper discusses three numerical integration schemes connected with a finite element solution to the transient heat‐conduction equation. The main emphasis is on the achievable accuracy. A simple recurrence relation derived from the Galerkin process is suggested for the treatment of fast‐varying boundary conditions as being significantly better than the usual Crank‐Nicholson scheme in matters of short‐time accuracy.