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anisotropic interpolation error estimate

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Some mixed finite element methodson anisotropic meshes
Mohamed Farhloul, Serge Nicaise, Luc Paquet
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 35 / Issue 5 / September 2001

Published online by Cambridge University Press:

15 April 2002, pp. 907-920

Print publication:

September 2001
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The paper deals with some mixed finite element methods on a classof anisotropic meshes based on tetrahedra and prismatic (pentahedral)elements. Anisotropic localinterpolation error estimates are derived in some anisotropic weighted Sobolevspaces. As particularapplications, the numerical approximation by mixed methods of the Laplace equationin domainswith edges is investigated where anisotropic finiteelement meshes are appropriate. Optimal error estimates are obtained using some anisotropic regularity results of thesolutions.