A four-field mixed finite element method for the Biot model and its solution algorithms
Duration: 47 mins 56 secs
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| Description: |
Yi, S-Y (University of Texas at El Paso)
Wednesday 8th June 2016 - 14:00 to 14:45 |
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| Created: | 2016-06-14 11:35 |
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| Collection: | Melt in the Mantle |
| Publisher: | Isaac Newton Institute |
| Copyright: | Yi, S-Y |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Co-author: Maranda L. Bean
In this talk, I will present a four-field mixed finite element method for the 2D Biot’s consolidation model of poroelasticity. The method is based on coupling two mixed finite element methods for each subproblem: the standard mixed finite element method for the flow subproblem and the Hellinger-Reissner formulation for the mechanical subproblem. Optimal a-priori error estimates are proved for both semi-discrete and fully discrete problems. In solving the coupled system, the two subproblems can be solved either simultaneously in a fully coupled scheme or sequentially in a loosely coupled scheme. I will present four iteratively coupled methods, known as drained, undrained, fixed-strain, and fixed-stress splits, in which the diffusion operator is separated from the elasticity operator and the two subproblems are solved in a staggered way while ensuring convergence of the solution. A-priori convergence results for each iterative coupling scheme will be proved and confirmed numerically. |
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