An a Posteriori Error Estimator for a New Stabilized Formulation of the Brinkman Problem

Autor:	Tomás P. Barrios, María González, Galina C. García, Rommel Bustinza
Rok vydání:	2014
Předmět:	Mathematical optimization Work (thermodynamics) A priori and a posteriori Estimator Uniqueness High order Porous media flow Least squares Projection (linear algebra) Mathematics
Zdroj:	Lecture Notes in Computational Science and Engineering ISBN: 9783319107042 ENUMATH
DOI:	10.1007/978-3-319-10705-9_25
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::77daa0a2fc771692ee6792093609bd42 https://doi.org/10.1007/978-3-319-10705-9_25 Zobrazit plný text záznamu