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- W2080495720 abstract "In this article we present a new implicit numerical scheme for reaction–diffusion–advection equations on an evolving in time hypersurface Γ(t). The partial differential equations are solved on a stationary quadrilateral, resp., hexahedral mesh. The zero level set of the time dependent indicator function ϕ(t) implicitly describes the position of Γ(t). The dominating convective-like terms, which are due to the presence of chemotaxis, transport of the cell density and surface evolution may lead to the non-positiveness of a given numerical scheme and in such a way cause appearance of negative values and give rise of nonphysical oscillations in the numerical solution. The proposed finite element method is constructed to avoid this problem: implicit treatment of corresponding discrete terms in combination with the algebraic flux correction (AFC) techniques make it possible to obtain a sufficiently accurate solution for reaction–diffusion–advection PDEs on evolving surfaces." @default.
- W2080495720 created "2016-06-24" @default.
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- W2080495720 date "2015-12-01" @default.
- W2080495720 modified "2023-10-16" @default.
- W2080495720 title "An AFC-stabilized implicit finite element method for partial differential equations on evolving-in-time surfaces" @default.
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- W2080495720 doi "https://doi.org/10.1016/j.cam.2015.03.002" @default.
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