Work

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

Year: 2025

Type: article

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.

Source: Journal of Numerical Mathematics

DOI: 10.1515/jnma-2024-0150

Authors: Markus Bachmayr, Simon Boisserée

Institution: RWTH Aachen University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funders: Deutsche Forschungsgemeinschaft, Johannes Gutenberg-Universität Mainz