An Adaptive Finite Difference Method for Hyperbolic Systems in OneSpace Dimension

A moving mesh numerical method for hyperbolic conservation laws

“…The first, which we will call the adaptive mesh approach, includes more meshpoints in the mesh wherever the approximate solution of (C) has large gradients; meshpoints are added and removed from the mesh when deemed necessary, but meshpoints are generally not moved from one timestep to the next, and the number of meshpoints may vary greatly over time. Öliger and his students [1], [2], [22], Lucier [18], and others (see [12]) have taken this approach. Osher and Sanders [24] have proved convergence for a method that uses this approach for conservation laws, but the rate of convergence of their method when used with any specific mesh selection algorithm is unknown.…”

Computational Methods for Continuum Models of Platelet Aggregation

“…The steep gradients are highly localized in regions that change with time. We are exploring the use of adaptive mesh refinement algorithms [4,3,2,14,5] in the x-and v-planes for the E equation to concentrate the computational effort in the most needed regions to yield well-resolved results for much less computational work.…”

A Moving Mesh Numerical Method for Hyperbolic Conservation Laws

“…The first, which we will call the adaptive mesh approach, includes more meshpoints in the mesh wherever the approximate solution of (C) has large gradients; meshpoints are added and removed from the mesh when deemed necessary, but meshpoints are generally not moved from one timestep to the next, and the number of meshpoints may vary greatly over time. Öliger and his students [1], [2], [22], Lucier [18], and others (see [12]) have taken this approach. Osher and Sanders [24] have proved convergence for a method that uses this approach for conservation laws, but the rate of convergence of their method when used with any specific mesh selection algorithm is unknown.…”