A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime

• Published in: arXiv.org
• Main Authors: Burman, Erik, Nechita, Mihai, Oksanen, Lauri
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 05.10.2019
• Subjects: Approximation; Computer Science - Numerical Analysis; Convection-diffusion equation; Dependence; Diffusion; Divergence; Estimates; Finite element analysis; Finite element method; Inverse problems; Mathematical analysis; Mathematics - Analysis of PDEs; Mathematics - Numerical Analysis; Nonlinear programming; Norms; Numerical analysis; Numerical stability; Upper bounds

The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit dependence on the Péclet number. A stabilized finite element m...