Numerical Companion to One-Sided p-Explicit Stability for High-Order Cut Finite Element Nitsche Methods

Abstract

This deposit is the numerical companion to “One-Sided p-Explicit Stability for High-Order Cut Finite Element Nitsche Methods” by Erik Burman, Peter Hansbo, Mats G. Larson and Karl Larsson. It contains Python experiment code, case parameters, compact reference data, reproducibility instructions and the Numerical Verification Guide. The implementation uses two-dimensional triangular Pp finite elements and CPU-based dense linear algebra. The studies cover polynomial continuation, one-sided flux estimates, penalty thresholds, convergence, numerical precision, Schwarz comparisons and exact tube certificates. The compact data retain 4,959 reference observations, 239 failed criteria and 22 tables, including known accuracy flags, the original solver-stopping failure and unresolved higher-degree attempts. Selected validation covers 15 numerical commands across ten study families; it is not a rerun of the full 257-command campaign or an audit of the omitted raw archives. Raw run archives and manuscript sources are not included. Detailed run records and exact certificates can be regenerated using the documented commands. The continuation and tube studies are tested on Apple Silicon macOS and Linux x86-64. The remaining supplied validation studies require the documented Linux configuration with a 64-bit longdouble significand and multiprocessing fork. The package includes file-integrity checks and pinned dependencies. Licensing is component-specific: Python code and software documentation are licensed under MIT; numerical data and the Numerical Verification Guide are licensed under CC BY 4.0. See LICENSE for the precise scope. AI assistance and author responsibility are disclosed in README.md. Source repository: KarlLarssonUmU/one-sided-hp-cutfemArchived commit: b6265c407371079d463d0c2ba18bcc3f1a658494.