Error estimates for moving least square approximations. (English) Zbl 0984.65096

We obtain error estimates for moving least square approximations in the one-dimensional case. For the application of this method to the numerical solution of differential equations it is fundamental to have error estimates for the approximations of derivatives. We prove that, under appropriate hypothesis on the weight function and the distribution of points, the method produces optimal order approximations of the function and its first and second derivatives. As a consequence, we obtain optimal order error estimates for Galerkin approximations of coercive problems. Finally, as an application of the moving least square method we consider a convection-diffusion equation and propose a way of introducing up-wind by means of a non-symmetric weight function. We present several numerical results showing the good behavior of the method.


65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
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