Numerical methods for convection-diffusion problems or The 30 years war

2013/06/21 by Martin Stynes, Stynes, Martin · 3 citations
Computer Science · Engineering · Mathematics · #65L #65N #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1306.5172

openalex publication_date 2013/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Convection-diffusion problems arise in the modelling of many physical processes. Their typical solutions exhibit boundary and/or interior layers. Despite the linear nature of the differential operator, these problems pose still-unanswered questions to the numerical analyst. This talk will give a selective overview of numerical methods for the solution of convection-diffusion problems, while placing them in a historical context. It examines the principles that underpin the competing numerical techniques in this area and presents some recent developments.

Cited by

• On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method
• Matrix-equation-based strategies for convection–diffusion equations
• Preconditioning of Active-Set Newton Methods for PDE-constrained Optimal Control Problems

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