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A note on pressure accuracy in immersed boundary method for Stokes flow. (English) Zbl 1416.76098

Summary: In this short note, we provide a simplified one-dimensional analysis and two-dimensional numerical experiments to predict that the overall accuracy for the pressure or indicator function in immersed boundary calculations is first-order accurate in \(L_{1}\) norm, half-order accurate in \(L_{2}\) norm, but has \(O(1)\) error in \(L_{\infty }\) norm. Despite the pressure has \(O(1)\) error near the interface, the velocity field still has the first-order convergence in immersed boundary calculations.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
65N06 Finite difference methods for boundary value problems involving PDEs
65N85 Fictitious domain methods for boundary value problems involving PDEs

Software:

FISHPAK
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Full Text: DOI

References:

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