A robust fully-mixed finite element method with skew-symmetry penalization for low-frequency poroelasticity
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908704905887744 |
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| author | Bonetti, Stefano Botti, Michele Vega, Patrick |
| author_facet | Bonetti, Stefano Botti, Michele Vega, Patrick |
| contents | In this work, we present and analyze a fully-mixed finite element scheme for the dynamic poroelasticity problem in the low-frequency regime. We write the problem as a four-field, first-order, hyperbolic system of equations where the symmetry constraint on the stress field is imposed via penalization. This strategy is equivalent to adding a perturbation to the saddle point system arising when the stress symmetry is weakly-imposed. The coupling of solid and fluid phases is discretized by means of stable mixed elements in space and implicit time advancing schemes. The presented stability analysis is fully robust with respect to meaningful cases of degenerate model parameters. Numerical tests validate the convergence and robustness and assess the performances of the method for the simulation of wave propagation phenomena in porous materials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_10192 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A robust fully-mixed finite element method with skew-symmetry penalization for low-frequency poroelasticity Bonetti, Stefano Botti, Michele Vega, Patrick Numerical Analysis 65N15, 65N30 In this work, we present and analyze a fully-mixed finite element scheme for the dynamic poroelasticity problem in the low-frequency regime. We write the problem as a four-field, first-order, hyperbolic system of equations where the symmetry constraint on the stress field is imposed via penalization. This strategy is equivalent to adding a perturbation to the saddle point system arising when the stress symmetry is weakly-imposed. The coupling of solid and fluid phases is discretized by means of stable mixed elements in space and implicit time advancing schemes. The presented stability analysis is fully robust with respect to meaningful cases of degenerate model parameters. Numerical tests validate the convergence and robustness and assess the performances of the method for the simulation of wave propagation phenomena in porous materials. |
| title | A robust fully-mixed finite element method with skew-symmetry penalization for low-frequency poroelasticity |
| topic | Numerical Analysis 65N15, 65N30 |
| url | https://arxiv.org/abs/2512.10192 |