Joint Mathematics Colloquium
Path-Conservative Numerical Methods and Well-Balanced Schemes: A Comprehensive Review
Speaker: Manuel J. Castro (Universidad de Málaga)Date: Wednesday, 08 April 2026 - 11:30Place: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Online: https://www.youtube.com/live/hLEpsmYBueI
Abstract:
In this talk, we briefly recall a comprehensive overview of high-order path-conservative and well-balanced schemes designed for hyperbolic systems. We review the Dal Maso-LeFloch-Murat theory to define weak solutions in systems containing nonconservative products or source terms. By leveraging this theoretical framework, we demonstrate how standard numerical schemes used for conservation laws can be successfully adapted to nonconservative problems. The presentation addresses the inherent theoretical challenges of defining and converging to weak solutions, outlines the extension of these methods to high-order accuracy, and validates the well-balanced property of the proposed methods through illustrative examples.
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