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Flexible finite‐difference stencils from isoparametric finite elements
Author(s) -
Frey William H.
Publication year - 1977
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.1620111103
Subject(s) - stencil , curvilinear coordinates , finite difference , mathematics , finite difference coefficient , finite difference method , grid , regular grid , finite element method , partial differential equation , context (archaeology) , mathematical analysis , generalization , polygon mesh , boundary value problem , geometry , mixed finite element method , computational science , paleontology , physics , biology , thermodynamics
A new finite‐difference technique for the numerical solution of boundary value problems for partial differential equations in two space variables is described. Isoparametric finite elements are used in a finite‐difference context to derive difference approximations to space derivatives on a locally curvilinear grid. The result is a generalization of a classical finite‐difference stencil which is ‘flexible’ in that it is adaptable to variable meshes, such as those arising from regions with curved boundaries. Numerical results presented for a test problem (potential flow past a circle) using a 9 × 10 grid agree with the analytic solution to within one per cent.