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A two‐grid characteristic finite volume element method for semilinear advection‐dominated diffusion equations
Author(s) -
Chen Chuanjun,
Liu Wei,
Bi Chunjia
Publication year - 2013
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.21766
Subject(s) - grid , mathematics , nonlinear system , finite volume method , finite element method , partial differential equation , advection , norm (philosophy) , mathematical analysis , space (punctuation) , diffusion , geometry , computer science , mechanics , physics , law , quantum mechanics , political science , thermodynamics , operating system
Abstract A two‐grid finite volume element method, combined with the modified method of characteristics, is presented and analyzed for semilinear time‐dependent advection‐dominated diffusion equations in two space dimensions. The solution of a nonlinear system on the fine‐grid space (with grid size h ) is reduced to the solution of two small (one linear and one nonlinear) systems on the coarse‐grid space (with grid size H ) and a linear system on the fine‐grid space. An optimal error estimate in H 1 ‐norm is obtained for the two‐grid method. It shows that the two‐grid method achieves asymptotically optimal approximation, as long as the mesh sizes satisfy h = O ( H 2 ). Numerical example is presented to validate the usefulness and efficiency of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013