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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.22 n.1 San José Jan./Jun. 2015


An adaptive wavelet-galerkin method for parabolic partial differential equations

Un método wavelet-galerkin adaptativo para ecuaciones diferenciales parciales parabólicas

Victoria Vampa*+, María T. Martín*


In this paper an Adaptive Wavelet-Galerkin method for the solution of parabolic partial differential equations modeling physical problems with different spatial and temporal scales is developed. A semi-implicit time difference scheme is applied and B-spline multiresolution structure on the interval is used. As in many cases these solutions are known to present localized sharp gradients, local error estimators are designed and an efficient adaptive strategy to choose the appropriate scale for each time is developed. Finally, experiments were performed to illustrate the applicability and efficiency of the proposed method.

Keywords: B-spline; multiresolution analysis; wavelet-Galerkin.


En este trabajo se desarrolla un método Wavelet-Galerkin Adaptativo para la resolución de ecuaciones diferenciales parabólicas que modelan problemas físicos, con diferentes escalas en el espacio y en el tiempo. Se utiliza un esquema semi-implícito en diferencias temporales y la estructura multirresolución de las B-splines sobre intervalo. Como es sabido que en muchos casos las soluciones presentan gradientes localmente altos, se han diseñado estimadores locales de error y una estrategia adaptativa eficiente para elegir la escala apropiada en cada tiempo. Finalmente, se realizaron experimentos que ilustran la aplicabilidad y la eficiencia del método propuesto.

Palabras clave: B-spline, análisis multirresolución; wavelet-Galerkin; ondeletas Galerkin.

Mathematics Subject Classification: 65M99.

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*Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata, Argentina. E-Mail:

Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina. IFLP-CCTCONICET, C. C. 727, 1900 La Plata, Argentina. E-Mail:

Received: 25/Feb/2014; Revised: 28/Aug/2014; Accepted: 19/Sep/2014

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