Scott–Vogelius–Nitsche Convergence for a Zero-Pressure-Gradient Problem on a Polygonally Approximated Boundary
Year: 2026
Type: preprint
Abstract: This repository contains the complete reproducibility package associated with the manuscript **“Scott–Vogelius–Nitsche convergence for a zero-pressure-gradient problem on a polygonally approximated boundary”** by Claudemir de Souza Cavalcante. The manuscript studies a two-dimensional Stokes benchmark with constant pressure in which the physical circular no-slip boundary is approximated by an inscribed polygon and the boundary condition is imposed weakly using a Nitsche formulation. The theoretical analysis establishes the error estimate \[\|u-u_h\|_{H^1(\Omega_h)}\le C\left(h_\Omega^k+h_\Gamma^{3/2}\right),\] for the stated Scott–Vogelius finite element setting and mesh assumptions. The geometric term arises from the interaction between the polygonal approximation of the circular boundary and the Nitsche consistency terms. The accompanying numerical study investigates the effective Nitsche penalty parameter using continuous quartic velocity elements and cubic divergence moments. Four computational meshes are considered. On the finest tested mesh, the computed coercivity transition occurs near \(\mu=60.3383\). The value \(\mu=100\) is coercive on all four meshes considered. This archive contains the material required to reproduce and independently check the computational results reported in the manuscript, including: - the manuscript source;- the complete numerical implementation;- scripts for reproducing the computations;- scripts for generating figures and tables;- the 52-row penalty-study CSV data;- numerical metadata and structural checks;- coefficient files for the four \(\mu=100\) solutions;- supplementary verification routines;- a README describing the computational environment and commands;- a SHA-256 manifest identifying the distributed files. The principal reproduction commands are python code/sv_nitsche_study.py --self-testpython code/sv_nitsche_study.py --outdir results/reproducedpython code/make_assets.py --results results/reproduced
Author: Cavalcante, Claudemir
Institution: Universidade Federal do Pará
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7207629167