Flexible finite‐difference stencils from isoparametric finite elements

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Abstract
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.