VEM-bubble discretisation and iterative coupling algorithm for a fluid induced seismicity model with rate-and-state friction
Abstract
This work addresses the discretisation and iterative coupling algorithm for an induced seismicity model accounting for fault reactivation and slip driven by subsurface fluid injection. The model couples single-phase Darcy flow in both the porous matrix and the fault network with a poroelastic mechanical response in the bulk and fault slip governed by a rate-and-state friction law. The contact mechanics problem is discretised using the Virtual Element Method with bubble stabilisation of the facewise constant Lagrange multiplier. It is combined with a Hybrid Finite Volume scheme for the mixed-dimensional Darcy flow model. The time discretisation is implicit and the nonlinear system is solved at each time step using an iterative coupling algorithm which iterates between the Darcy flow, the frictional contact-mechanics, and the state differential equation. The contraction of this iterative coupling algorithm is established with a smallness assumption on the time step independent on the mesh size. This proves convergence of the fixed-point as well as well-posedness of the system. The frictional contact-mechanical model is solved using a Newton-Raphson algorithm based on a local nonlinear inversion of the friction rate-and-state law and a block Gauss-Seidel preconditioner exploiting the structure of the VEM-bubble-P 0 mixed discretisation.
Related
- An existence result of a functional integral equation via Darbo type theorem and an iterative algorithm to solve it
- Iterative coupling schemes for mixed-dimensional poromechanical models with frictional contact: convergence analysis and adaptive stabilization
- Discretisation in algebraic K-theory of independent ample groupoids and their Steinberg algebras
- Uniform approximation of spectra of linear second order differential operators via discrete sine transform based discretisation
- Optimal Refinement in Dynamic Discretisation Discovery for Continuous-Time Service Network Design
BibTeX
@misc{zerga2026vembubble,
title = {{VEM-bubble discretisation and iterative coupling algorithm for a fluid induced seismicity model with rate-and-state friction}},
author = {El Hadi Zerga and Roland Masson and Jean Paul Ampuero and Pierre Romanet},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05787533v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - VEM-bubble discretisation and iterative coupling algorithm for a fluid induced seismicity model with rate-and-state friction
AU - El Hadi Zerga
AU - Roland Masson
AU - Jean Paul Ampuero
AU - Pierre Romanet
PY - 2026
DA - 2026/10/08
PB - HAL
UR - https://hal.science/hal-05787533v1
AB - This work addresses the discretisation and iterative coupling algorithm for an induced seismicity model accounting for fault reactivation and slip driven by subsurface fluid injection. The model couples single-phase Darcy flow in both the porous matrix and the fault network with a poroelastic mechanical response in the bulk and fault slip governed by a rate-and-state friction law. The contact mechanics problem is discretised using the Virtual Element Method with bubble stabilisation of the facewise constant Lagrange multiplier. It is combined with a Hybrid Finite Volume scheme for the mixed-dimensional Darcy flow model. The time discretisation is implicit and the nonlinear system is solved at each time step using an iterative coupling algorithm which iterates between the Darcy flow, the frictional contact-mechanics, and the state differential equation. The contraction of this iterative coupling algorithm is established with a smallness assumption on the time step independent on the mesh size. This proves convergence of the fixed-point as well as well-posedness of the system. The frictional contact-mechanical model is solved using a Newton-Raphson algorithm based on a local nonlinear inversion of the friction rate-and-state law and a block Gauss-Seidel preconditioner exploiting the structure of the VEM-bubble-P 0 mixed discretisation.
ER -