Flexible finite‐difference stencils from isoparametric finite elements

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.