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Book Chapter10.1007/978-3-0348-5328-6_11

Finite Element Methods in Conduction-Convection Problems

A. R. Mitchell-1976-01-01-Birkhäuser Basel eBooks
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TL;DRAbstract

Galerkin finite element methods based on symmetric pyramid basis functions do not give good answers when applied to second order elliptic equations with large coefficients of the first order terms. This is particularly so when the mesh size is large. In the present study asymmetric linear basis functions are introduced which overcome this difficulty. In addition, parabolic basis functions are shown to be oscillation free and highly accurate for the working range of mesh sizes.

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Galerkin finite element methods based on symmetric pyramid basis functions do not give good answers when applied to second order elliptic equations with large coefficients of the first order terms. This is particularly so when the mesh size is large. In the present study asymmetric linear basis functions are introduced which overcome this difficulty. In addition, parabolic basis functions are shown to be oscillation free and highly accurate for the working range of mesh sizes.

Keywords

Basis functionFinite element methodGalerkin methodBasis (linear algebra)MathematicsMathematical analysisDiscontinuous Galerkin methodOscillation (cell signaling)

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