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A monotone conservative Eulerian–Lagrangian scheme for reaction‐diffusion‐convection equations modeling chemotaxis
Author(s) -
Smiley Michael W.
Publication year - 2007
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.20185
Subject(s) - monotone polygon , mathematics , convection–diffusion equation , convergence (economics) , grid , eulerian path , partial differential equation , lagrangian , diffusion , stability (learning theory) , consistency (knowledge bases) , partial derivative , convection , mathematical analysis , geometry , computer science , mechanics , physics , machine learning , economics , thermodynamics , economic growth
A numerical method for convection dominated diffusion problems, that exploits the use of characteristics, is derived and analyzed. It is shown to preserve positivity of solutions and be locally mass conserving. Stability, consistency and order one convergence are verified. Because of the way in which it determines characteristic pre‐images of grid cells, the method can be easily implemented for 1‐, 2‐, or 3‐dimensional problems on rectangular grids.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007