Approximating partial derivatives of first and second order by quadratic spline quasi-interpolants on uniform meshes

Authors:
Françoise Foucher;Paul Sablonnière
Affiliations:
Laboratoire de Mathématiques Jean Leray, Ecole Centrale de Nantes, BP 92101, 44321 Nantes Cedex 3, France;Centre de Mathématiques, INSA de Rennes, CS 14315, 35043 Rennes Cedex, France
Venue:
Mathematics and Computers in Simulation
Year:
2008

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Abstract

Given a bivariate function f defined in a rectangular domain @W, we approximate it by a C^1 quadratic spline quasi-interpolant (QI) and we take partial derivatives of this QI as approximations to those of f. We give error estimates and asymptotic expansions for these approximations. We also propose a simple algorithm for the determination of stationary points, illustrated by a numerical example.