Analysis and Elimination of Numerical Pressure Dependency in Coupled Stokes-Darcy Problem

Fuente: arXiv
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Main Author: Zhang, Jiachuan
Format: Preprint
Published: 2025
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author Zhang, Jiachuan
author_facet Zhang, Jiachuan
contents This paper analyses the classical mixed finite element method (FEM) and a pressure-robust variant with divergence-free reconstruction operators for the coupled Stokes-Darcy problem. Its main contribution is to provide viscosity-explicit a priori error estimates that clearly distinguish the pressure dependence of the two discretizations: the velocity error of the classical scheme depends on both the exact pressure and the viscosity, whereas the pressure-robust method eliminates both entirely. Moreover, we derive pressure error estimates and quantify their dependence on the exact solution and model parameters. Two-dimensional numerical experiments validate the theoretical findings, including higher-order tests up to polynomial degree three and a lid-driven cavity benchmark with a piecewise linear interface. The implementation code is made publicly available to facilitate reproducibility.
format Preprint
id arxiv_https___arxiv_org_abs_2504_19116
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Analysis and Elimination of Numerical Pressure Dependency in Coupled Stokes-Darcy Problem
Zhang, Jiachuan
Numerical Analysis
This paper analyses the classical mixed finite element method (FEM) and a pressure-robust variant with divergence-free reconstruction operators for the coupled Stokes-Darcy problem. Its main contribution is to provide viscosity-explicit a priori error estimates that clearly distinguish the pressure dependence of the two discretizations: the velocity error of the classical scheme depends on both the exact pressure and the viscosity, whereas the pressure-robust method eliminates both entirely. Moreover, we derive pressure error estimates and quantify their dependence on the exact solution and model parameters. Two-dimensional numerical experiments validate the theoretical findings, including higher-order tests up to polynomial degree three and a lid-driven cavity benchmark with a piecewise linear interface. The implementation code is made publicly available to facilitate reproducibility.
title Analysis and Elimination of Numerical Pressure Dependency in Coupled Stokes-Darcy Problem
topic Numerical Analysis
url https://arxiv.org/abs/2504.19116