An a Posteriori Error Estimator for a New Stabilized Formulation of the Brinkman Problem
We present in this work an a posteriori error estimator for a porous media flow problem that follows the Brinkman model. First, we introduce the pseudostress as an auxiliary unknown, which let us to eliminate the pressure and thus derive a dual-mixed formulation in velocity-pseudostress. Next, in or...
| Autor Principal: | García, Galina |
|---|---|
| Otros Autores: | Barrios, Tomás, González, María |
| Formato: | Artículo |
| Idioma: | English |
| Publicado: |
Springer
2015
|
| Acceso en línea: |
Numerical Mathematics and Advanced Applications - ENUMATH 2013 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: |
We present in this work an a posteriori error estimator for a porous media flow problem that follows the Brinkman model. First, we introduce the pseudostress as an auxiliary unknown, which let us to eliminate the pressure and thus derive a dual-mixed formulation in velocity-pseudostress. Next, in order to circumvent an inf-sup condition for the unique solvability, we stabilize the scheme by adding some appropriate least squares terms. The existence and uniqueness of solution are guaranteed and we derive an a posteriori error estimator based on the Ritz projection of the error, which is reliable and efficient up to high order terms. Finally, we report one numerical example confirming the good properties of the estimator. |
|---|