A stabilized mixed method applied to Stokes system with nonhomogeneous source terms: The stationary case Dedicated to Prof. R. Rodríguez,on the occasion of his 65th birthday |
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| Authors: | Tomás P Barrios Edwin M Behrens Rommel Bustinza |
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| Institution: | 1. Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Concepción, Chile;2. Departamento de Ingeniería Civil, Universidad Católica de la Santísima Concepción, Concepción, Chile;3. Centro de Investigación en Ingeniería Matemática (CI2MA) & Departamento de Ingeniería Matemática, Universidad de Concepción, Concepción, Chile |
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| Abstract: | This article is concerned with the Stokes system with nonhomogeneous source terms and nonhomogeneous Dirichlet boundary condition. First, we reformulate the problem in its dual mixed form, and then, we study its corresponding well-posedness. Next, in order to circumvent the well-known Babuška-Brezzi condition, we analyze a stabilized formulation of the resulting approach. Additionally, we endow the scheme with an a posteriori error estimator that is reliable and efficient. Finally, we provide numerical experiments that illustrate the performance of the corresponding adaptive algorithm and support its use in practice. |
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| Keywords: | a posteriori error estimates augmented mixed formulation Ritz projection of the error |
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