Premium
Nonconforming finite element methods with subgrid viscosity applied to advection‐diffusion‐reaction equations
Author(s) -
El Alaoui Linda,
Ern Alexandre
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.20146
Subject(s) - mathematics , finite element method , advection , finite volume method , viscosity , partial differential equation , polygon mesh , convection–diffusion equation , norm (philosophy) , mixed finite element method , diffusion , mathematical analysis , geometry , mechanics , physics , thermodynamics , political science , law
A nonconforming (Crouzeix–Raviart) finite element method with subgrid viscosity is analyzed to approximate advection‐diffusion‐reaction equations. The error estimates are quasi‐optimal in the sense that keeping the Péclet number fixed, the estimates are suboptimal of order ${1\over 2}$ in the mesh size for the L 2 ‐norm and optimal for the advective derivative on quasi‐uniform meshes. The method is also reformulated as a finite volume box scheme providing a reconstruction formula for the diffusive flux with local conservation properties. Numerical results are presented to illustrate the error analysis. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006