A stabilized mixed finite element method for Darcy flow |
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| Affiliation: | 1. Department of Civil and Materials Engineering, The University of Illinois at Chicago, Chicago, IL 60607-7023, USA;2. Department of Mechanical Engineering, Division of Mechanics and Computations, Stanford University, Stanford, CA 94305, USA;1. Université Paris Est, IFSTTAR, 10-14 Bd Newton, Cité Descartes, 77447 Marne La Vallée Cedex, France;2. CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France;3. UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France;4. Institut Universitaire de France and Division of Applied Mathematics, Brown University, Providence, RI, USA;1. Department of Mathematics, BITS Pilani-KK Birla Goa Campus, Zuarinagar, Goa-403726, India;2. Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram-695547, Kerala, India |
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| Abstract: | ![]()
We develop new stabilized mixed finite element methods for Darcy flow. Stability and an a priori error estimate in the “stability norm” are established. A wide variety of convergent finite elements present themselves, unlike the classical Galerkin formulation which requires highly specialized elements. An interesting feature of the formulation is that there are no mesh-dependent parameters. Numerical tests confirm the theoretical results. |
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