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The characteristic finite element alternating direction method with moving meshes for nonlinear convection‐dominated diffusion problems
Author(s) -
Yuan Yirang
Publication year - 2006
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.20118
Subject(s) - polygon mesh , finite element method , mathematics , computation , nonlinear system , norm (philosophy) , convection–diffusion equation , mathematical analysis , geometry , algorithm , physics , quantum mechanics , political science , law , thermodynamics
In modern numerical simulation of prospecting and exploiting oil‐gas resources and in environmental science, it is necessary to consider numerical method of nonlinear convection‐dominated diffusion problems. This thesis, starting from actual conditions such as the three‐dimensional characteristics of large‐scale science‐engineering computation, puts forward a kind of characteristic finite element alternating direction method with moving meshes. Some techniques, such as calculus of variations, operator‐splitting, generalized L 2 projection, energy method, negative norm estimate, the theory of prior estimates and techniques, are adopted. Optimal order estimates in L 2 norm are derived to determine the errors in the approximate solution. Thus the important theoretical problem has been solved. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005