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Cubic spline Galerkin approximations to parabolic systems with coupled non‐linear boundary conditions
Author(s) -
Murphy W. D.
Publication year - 1975
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.1620090106
Subject(s) - galerkin method , finite element method , mathematics , boundary value problem , partial differential equation , mathematical analysis , spline (mechanical) , work (physics) , boundary (topology) , finite difference , parabolic partial differential equation , structural engineering , engineering , mechanical engineering
This paper describes a practical implementation of the Galerkin finite element procedure for solving systems of parabolic partial differential equations with non‐linear boundary conditions. This technique consists of finding an approximation in the form of a finite sum of cubic B‐splines, which yield high‐order accurate results, and consequently, solutions can be developed with remarkable precision and speed up to the steady state region where conventional finite difference methods often fail. In addition, the choice of mesh width and nodal spacing can be automatically determined for a predictor‐corrector routine, thereby relieving the engineer of a great deal of ‘guess work’ that is normally characteristic of solving such problems.