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Exponentially fitted discontinuous Galerkin schemes for singularly perturbed problems |
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| Authors: | Ariel L Lombardi Paola Pietra |
| Institution: | 1. Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, Los Polvorines, B1613GSX Provincia de Buenos Aires, Argentina;2. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, ArgentinaFirst author is member of CONICET, Argentina;3. Istituto di Matematica Applicata e Tecnologie Informatiche ‐ CNR, Via Ferrata 1, I‐27100 Pavia, Italy |
| Abstract: | New discontinuous Galerkin schemes in mixed form are introduced for symmetric elliptic problems of second order. They exhibit reduced connectivity with respect to the standard ones. The modifications in the choice of the approximation spaces and in the stabilization term do not spoil the error estimates. These methods are then used for designing new exponentially fitted schemes for advection dominated equations. The presented numerical tests show the good performances of the proposed schemes. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011 |
| Keywords: | advection‐diffusion equations discontinuous Galerkin methods exponentially fitted schemes |