Work

On Smooth Solution to Three-Dimensional Incompressible Navier–Stokes Equations Based on Numerical Solutions by Finite Element Approximation

Year: 2025

Type: article

Abstract: In this paper, we develop a fully discrete finite element scheme, based on a second-order backward differentiation formula (BDF2), for numerically solving the three-dimensional incompressible Navier–Stokes equations. Under the assumption that the fully discrete solution remains bounded in a certain norm, we establish that any smooth initial data necessarily gives rise to a unique strong solution that remains smooth. Moreover, we demonstrate that the fully discrete numerical solution converges strongly to this exact solution as the temporal and spatial discretization parameters approach zero.

Source: Mathematics

DOI: 10.3390/math13193236

Authors: Fengnan Liu, Junpeng Cao, Ziqiu Zhang

Institutions: Dalian University of Technology, Northeastern University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Dalian University of Technology