An H(div)-conforming Finite Element Method for Biot's Consolidation Model
| Autor: | Mingchao Cai, Feng Wang, Yuping Zeng |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Discretization
Consolidation (soil) Biot number Applied Mathematics Mathematical analysis Poromechanics 010103 numerical & computational mathematics 01 natural sciences Finite element method Article 010101 applied mathematics Rate of convergence Discontinuous Galerkin method Uniqueness 0101 mathematics Mathematics |
| Zdroj: | East Asian journal on applied mathematics. 9(3) |
| ISSN: | 2079-7362 |
| Popis: | In this paper, we develop an H(div)-conforming finite element method for Biot’s consolidation model in poroelasticity. In our method, the flow variables are discretized by an H(div)-conforming mixed finite elements. For relaxing the H(1)-conformity of the displacement, we approximate the displacement by using an H(div)-conforming finite element method, in which the tangential components are discretized in the interior penalty discontinuous Galerkin framework. For both the semi-discrete and the fully discrete schemes, we prove the existence and uniqueness theorems of the approximate solutions and derive the optimal convergence rate for each variable. |
| Databáze: | OpenAIRE |
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