A Nonconforming Finite Element Method with Face Penalty for Advection—Diffusion Equations

L. El Alaoui (), A. Ern () and E. Burman ()
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L. El Alaoui: Imperial College, Department of Mathematics
A. Ern: ENPC, CERMICS
E. Burman: EPFL, CMCS/IACS

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 512-519 from Springer

Abstract: Abstract We present a nonconforming finite element method with face penalty to approximate advection-diffusion-reaction equations. The a priori error analysis leads to (quasi-)optimal error estimates in the mesh-size keeping the Péclet number fixed. The a posteriori error analysis yields residual-type error indicators that are semi-robust in the sense that the lower and upper bounds of the error differ by a factor bounded by the square root of the Péclet number. Finally, to illustrate the theory, numerical results including adaptively generated meshes are presented.

Keywords: Posteriori Error; Posteriori Error Estimate; Galerkin Approximation; Error Indicator; Posteriori Error Estimator (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-34288-5_47

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DOI: 10.1007/978-3-540-34288-5_47

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