Abstract
In this paper we consider a class of “filtered” schemes for some first order time dependent Hamilton-Jacobi equations. A typical feature of a filtered scheme is that at the node x j the scheme is obtained as a mixture of a high-order scheme and a monotone scheme according to a filter function F. The mixture is usually governed by F and by a fixed parameter ε = ε(Δt, Δx) > 0 which goes to 0 as (Δt, Δx) is going to 0 and does not depend on n. Here we improve the standard filtered scheme introducing an adaptive and automatic choice of the parameter ε = ε n(Δt, Δx) at every iteration. To this end, we use a smoothness indicator in order to select the regions where we can compute the regularity threshold ε n. The numerical tests presented confirms the effectiveness of the adaptive scheme.
All the authors are members of the INdAM Research group GNCS.
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Falcone, M., Paolucci, G., Tozza, S. (2019). Adaptive Filtered Schemes for First Order Hamilton-Jacobi Equations. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_34
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DOI: https://doi.org/10.1007/978-3-319-96415-7_34
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