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An Eulerian‐Lagrangian single‐node collocation method for transient advection‐diffusion equations in multiple space dimensions
Author(s) -
Wu Li,
Wang Hong
Publication year - 2004
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10094
Subject(s) - collocation (remote sensing) , mathematics , partial differential equation , eulerian path , orthogonal collocation , advection , collocation method , transient (computer programming) , diffusion , partial derivative , mathematical analysis , space (punctuation) , method of characteristics , node (physics) , numerical analysis , lagrangian , differential equation , ordinary differential equation , computer science , physics , quantum mechanics , machine learning , operating system , thermodynamics
We developed a nonconventional Eulerian‐Lagrangian single‐node collocation method for transient advection‐diffusion transport partial differential equations in multiple space dimensions. This method greatly reduces the number of unknowns in conventional collocation method, generates accurate numerical solutions, and allows large time steps to be used in numerical simulations. We perform numerical experiments to show the strong potential of the method. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 284–301, 2004