Regularization errors in the resolution of elliptic equations in the presence of discontinuities and interfacial sources
Year: 2025
Type: article
Abstract: In this work we present a systematic analysis of the errors introduced in the solution of elliptic equations by the regularization of discontinuous coefficients, jumps on the primitive variable and interfacial flux sources. By decomposing the system into an outer region and an inner region where regularization takes place within a small fixed distance, we show that it is possible to find continuum models where the lower order errors introduced by the regularization procedure remain confined within the regularization region, guaranteeing the convergence of the solution in the outer regions. In addition, the analysis presented provides regularization error estimates that can be eventually used to suppress the errors introduced by any regularization method at arbitrary order both in the inner and outer regions. Various analytical and numerical examples are provided to validate the results of the error models proposed.
Source: Journal of Computational Physics
Authors: Daniel Fuster, Eric Sultan
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,980
OpenAlex ID: W4415727804