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 xj 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.

Maurizio Falcone, PAOLUCCI, G., Silvia Tozza (2019). Adaptive Filtered Schemes for First Order Hamilton-Jacobi Equations. Springer Nature Switzerland AG 2019 [10.1007/978-3-319-96415-7_34].

Adaptive Filtered Schemes for First Order Hamilton-Jacobi Equations

Silvia Tozza
2019

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 xj 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.
2019
Numerical Mathematics and Advanced Applications ENUMATH 2017
389
398
Maurizio Falcone, PAOLUCCI, G., Silvia Tozza (2019). Adaptive Filtered Schemes for First Order Hamilton-Jacobi Equations. Springer Nature Switzerland AG 2019 [10.1007/978-3-319-96415-7_34].
Maurizio Falcone; PAOLUCCI, GIULIO; Silvia Tozza
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/844062
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