An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities

TL;DR

This paper introduces an adaptive space-time numerical method for nonlinear poroviscoelastic flows with discontinuous porosities, combining Picard iteration and least-squares formulation for efficient and convergent solutions.

Contribution

It presents a novel adaptive method that handles discontinuous initial porosities and provides computable error bounds for nonlinear porous media flows.

Findings

Efficient approximation of localized porosity waves.

Optimal convergence with respect to degrees of freedom.

Effective handling of discontinuous initial porosities.

Abstract

This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent method that yields computable error bounds is constructed by a combination of Picard iteration and a least-squares formulation. The adaptive scheme permits spatially variable time steps, which in numerical tests are shown to lead to efficient approximations of solutions with localized porosity waves. The method is also observed to exhibit optimal convergence with respect to the total number of spatio-temporal degrees of freedom.