On the role of global conservation property for finite difference schemes. (English) Zbl 07512378
Summary: High-order finite difference schemes are widely used in the field of numerical solutions of partial differential equations. Although the importance of their local conservation property is well recognized, especially for solving hyperbolic conservation laws, the importance of their global conservation property (GCP) is seldom considered. To show that in some cases the GCP is indeed important in improving performance of finite difference schemes, we make a comparative study of two fifth-order schemes with boundary closures satisfying the GCP or not. For some toy models considered in this short note, we show that the scheme satisfying the GCP does perform better than its counterpart without the GCP.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 76Mxx | Basic methods in fluid mechanics |
| 35Lxx | Hyperbolic equations and hyperbolic systems |
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