Abstract
We propose numerical schemes that enable the application of particle methods for advection problems in general bounded domains. These schemes combine particle fields with Cartesian tensor product splines and a fictitious domain approach. Their implementation only requires a fitted mesh of the domain’s boundary, and not the domain itself, where an unfitted Cartesian grid is used. We establish the stability and consistency of these schemes in Ws,p-norms, s ∈ ℝ, 1 ≤ p ≤ ∞.
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