Guaranteed a posteriori error estimates for a fractured porous medium
| Autor: | Zoubida Mghazli, Ilyas Naji |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Numerical Analysis
Work (thermodynamics) General Computer Science Applied Mathematics Context (language use) 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Upper and lower bounds Finite element method Mathematics::Numerical Analysis Theoretical Computer Science Flow (mathematics) Modeling and Simulation 0202 electrical engineering electronic engineering information engineering Fracture (geology) Applied mathematics A priori and a posteriori 020201 artificial intelligence & image processing 0101 mathematics Porous medium Mathematics |
| Zdroj: | Mathematics and Computers in Simulation. 164:163-179 |
| ISSN: | 0378-4754 |
| DOI: | 10.1016/j.matcom.2019.02.002 |
| Popis: | We present in this work a posteriori error estimates for a reduced model problem of flow in fractured porous media approximated by the Raviart–Thomas mixed finite element of lowest order. The fracture assumed to be sufficiently thin to be approximated by a one-dimensional interface, leading to a coupled 2D/1D problem. The a posteriori error estimates developed here are based on the technique of postprocessing and lead to an upper bound of the error by some indicators with 1 as a multiplicative constant. In the context of our approximation, since the velocity is well approximated, we will consider only a reconstruction of the pressure. Numerical results show that all indicators converge to zero when the mesh size goes to zero, and are useful for mesh adaptation. |
| Databáze: | OpenAIRE |
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