A least-squares finite element scheme for the RLW equation. (English) Zbl 0867.76040
Summary: The regularized long wave (RLW) equation is solved by a least-squares technique using linear space-time finite elements. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent difference scheme based on cubic spline interpolation functions. In addition, for very small amplitude waves \((\leq 0\cdot 09)\), it has higher accuracy than an approach using quadratic \(B\)-spline finite element within Galerkin’s method. The development of an undular bore is modelled.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76D33 | Waves for incompressible viscous fluids |
| 86A05 | Hydrology, hydrography, oceanography |
Keywords:
development of undular bore; variational principle; linear space-time finite elements; single solitary waveReferences:
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