# A high-order discretization of nonlinear poroelasticity

## TL;DR

This paper presents a novel high-order discretization method for nonlinear poroelasticity that is stable, flexible on complex meshes, and efficient, enabling accurate simulations of fluid flow in deformable porous media.

## Contribution

It introduces a nonconforming high-order discretization combining Hybrid High-Order and discontinuous Galerkin methods for nonlinear poroelasticity, supporting arbitrary orders and complex geometries.

## Key findings

- The method is stable and accurate in 2D and 3D.
- It handles complex meshes including polyhedral elements.
- It allows for reduced computational cost through static condensation.

## Abstract

In this work we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. The nonlinear elasticity operator is discretized using a Hybrid High-Order method, while the Darcy operator relies on a Symmetric Weighted Interior Penalty discontinuous Galerkin scheme. The method is valid in two and three space dimensions, delivers an inf-sup stable discretization on general meshes including polyhedral elements and nonmatching interfaces, supports arbitrary approximation orders, and has a reduced cost thanks to the possibility of statically condensing a large subset of the unknowns for linearized versions of the problem. Moreover, the proposed construction can handle both nonzero and vanishing specific storage coefficients.