An Apriori-a Posteriori Numerical Approach to Nonlinear Hyperbolic Conservation Laws
Abstract
This project aimed first at obtaining a better understanding of numerical methods for hyperbolic conservation laws. Several significant advances were obtained. In particular, the interplay between the size, uniformity and topology of numerical grids and the accuracy of numerical solutions based on those grids has been uncovered. This type of results in unique for problems with low regularity. Those a priori estimates have led to the first explanation of supraconvergence for conservation laws. The possibility of using earlier results, a posteriori estimates, for the design of adaptive methods with full mathematical backing was also investigated. In a second part. numerical methods for related problems were considered. For systems of Hamilton-Jacobi equations, the notion of viscosity solution cannot be applied. In spite of this, competitive numerical methods were constructed and successfully used. The flow of granular materials, a highly important but ill-understood problem, was also considered. Those problems have several nonstandard features. Computational results based on the first implementation, in that field, of higher order numerical (Discontinuous Galerkin) methods were obtained. A code is currently being tested by engineers in an industrial setting.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1999
- Accession Number
- ADA369981
Entities
People
- Pierre A. Gremaud
Organizations
- North Carolina State University