Klein-Gordon equation with advection on unbounded domains using spectral elements and high-order non-reflecting boundary conditions
Giraldo, Francis X.
Lindquist, Joseph M.
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A reduced shallow water model under constant, non-zero advection in the infinite channel is considered. High-order (Givoli–Neta) non-reflecting boundary conditions are introduced in various configurations to create a finite computational space and solved using a spectral element formulation with high-order time integration. Numerical examples are used to demonstrate the synergy of using high-order spatial, time, and boundary discretization. We show that by balancing all numerical errors involved, high-order accuracy can be achieved for unbounded domain problems.
Applied Mathematics and Computation, 217, (2010), 2710–2723.The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2010.07.079