Abstract
We develop a characteristic-based domain decomposition and space-time local refinement method for first-order linear hyperbolic equations. The method naturally incorporates various physical and numerical interfaces into its formulation and generates accurate numerical solutions even if large time-steps are used. The method fully utilizes the transient and strongly local behavior of the solutions of hyperbolic equations and provides solutions with significantly improved accuracy and efficiency. Several numerical experiments are presented to illustrate the performance of the method and for comparison with other domain decomposition and local refinement schemes.
Original language | English |
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Pages (from-to) | 1-28 |
Number of pages | 28 |
Journal | Numerical Methods for Partial Differential Equations |
Volume | 15 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 1999 |
Keywords
- Adaptive refinement; advection
- Lagrangian methods; linear hyperbolic problems; local refinement techniques
- Reaction equations; characteristic methods; domain decomposition methods; Eulerian
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics