Artículo
Armentano, M.G.; Durán, R.G. "Error estimates for moving least square approximations" (2001) Applied Numerical Mathematics. 37(3):397-416
Consulte la política de Acceso Abierto del editor
Abstract:
In this paper 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. © 2001 IMACS.
Registro:
| Documento: | Artículo |
| Título: | Error estimates for moving least square approximations |
| Autor: | Armentano, M.G.; Durán, R.G. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, 1428 Buenos Aires, Argentina |
| Palabras clave: | Convection-diffusion; Error estimates; Galerkin approximations; Moving least square; Differential equations; Error analysis; Galerkin methods; Problem solving; Theorem proving; Moving least square approximation; Least squares approximations |
| Año: | 2001 |
| Volumen: | 37 |
| Número: | 3 |
| Página de inicio: | 397 |
| Página de fin: | 416 |
| DOI: | http://dx.doi.org/10.1016/S0168-9274(00)00054-4 |
| Título revista: | Applied Numerical Mathematics |
| Título revista abreviado: | Appl Numer Math |
| ISSN: | 01689274 |
| CODEN: | ANMAE |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01689274_v37_n3_p397_Armentano |
Referencias:
- Belytschko, T., Lu, Y.Y., Gu, L., A new implementation of the element free Galerkin method (1994) Comput. Methods Appl. Mech. Eng., 113, pp. 397-414
- Belytschko, T., Krysl, P., Element-free Galerkin method: Convergence of the continuous and discontinuous shape functions (1997) Comput. Methods Appl. Mech. Eng., 148, pp. 257-277
- Brenner, S.C., Scott, L.R., (1994) The Mathematical Theory of Finite Element Methods, , Springer, New York
- Ciarlet, P.G., (1978) The Finite Element Method for Elliptic Problems, , North-Holland, Amsterdam
- Johnson, L.W., Riess, R.D., (1982) Numerical Analysis, , Addison-Wesley, Reading, MA
- Lancaster, P., Salkauskas, K., Surfaces generated by moving least squares methods (1981) Math. Comp., 37, pp. 141-158
- Levin, D., The approximation power of moving least-squares (1998) Math. Comp., 67, pp. 1335-1754
- Marano, M., (1986) Mejor aproximación local, , Tesis de Doctorado en Matemáticas, U. N. de San Luis
- Motzkin, T.S., Walsh, J.L., Polynomials of best approximation on a real finite point set (1959) Trans. Am. Math. Soc., 91, pp. 231-245
- Rice, J.R., Best approximation and interpolating functions (1961) Trans. Amer. Math. Soc., 101, pp. 477-498
- Roos, H.G., Stynes, M., Tobiska, L., (1996) Numerical Methods for Singularity Perturbed Differential Equations, , Springer
- Shepard, D., A two-dimensional interpolation function for irregularly spaced points (1968) Proc. ACM Natl. Conf., pp. 517-524
- Taylor, R., Zienkiewicz, O.C., Oñate, E., Idelsohn, S., (1995) Moving least square approximations for the solution of differential equations, , Technical Report, CIMNE
Citas:
---------- APA ----------
Armentano, M.G. & Durán, R.G. (2001) . Error estimates for moving least square approximations. Applied Numerical Mathematics, 37(3), 397-416.http://dx.doi.org/10.1016/S0168-9274(00)00054-4
---------- CHICAGO ----------
Armentano, M.G., Durán, R.G. "Error estimates for moving least square approximations" . Applied Numerical Mathematics 37, no. 3 (2001) : 397-416.http://dx.doi.org/10.1016/S0168-9274(00)00054-4
---------- MLA ----------
Armentano, M.G., Durán, R.G. "Error estimates for moving least square approximations" . Applied Numerical Mathematics, vol. 37, no. 3, 2001, pp. 397-416.http://dx.doi.org/10.1016/S0168-9274(00)00054-4
---------- VANCOUVER ----------
Armentano, M.G., Durán, R.G. Error estimates for moving least square approximations. Appl Numer Math. 2001;37(3):397-416.http://dx.doi.org/10.1016/S0168-9274(00)00054-4
