A decoupling and linearizing discretization for weakly coupled poroelasticity with nonlinear permeability

TL;DR

This paper introduces a semi-explicit, first-order discretization scheme for weakly coupled poroelasticity with nonlinear permeability, achieving decoupling and linearization to enhance computational efficiency while maintaining optimal convergence.

Contribution

It presents a novel decoupling and linearizing discretization method for weakly coupled poroelasticity with nonlinear permeability, eliminating the need for inner iterations.

Findings

Achieves twofold computational speed-up.

Maintains optimal first-order convergence.

Effectively handles various nonlinear permeability relations.

Abstract

We analyze a semi-explicit time discretization scheme of first order for poro\-elasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled. The approach leads to a decoupling of the equations and, at the same time, linearizes the nonlinearity without the need of further inner iteration steps. Hence, the computational speed-up is twofold without a loss in the convergence rate. We prove optimal first-order error estimates by considering a related delay system and investigate the method numerically for different examples with various types of nonlinear displacement-permeability relations.