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BIT Numerical Mathematics
Published in: BIT Numerical Mathematics 4/2014

01-12-2014

Supercloseness of the mixed finite element method for the primary function on unstructured meshes and its applications

Author: JaEun Ku

Published in: BIT Numerical Mathematics | Issue 4/2014

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Abstract

We establish that the approximate solution of the mixed finite element method for the primary function is superconvergent to its \(L_2\) local projection on unstructured meshes. To the best of our knowledge, all of the superconvergent results concerning mixed method need some conditions such as requiring the underlying meshes to be structured or using higher-order approximation spaces. Our results are valid on shape regular meshes, and any order of approximation spaces can be used. As an elementary consequence, we provide a proof that solutions of least-squares (LS) finite element method are higher-order perturbations of the solutions of the mixed and standard Galerkin methods. Also, we provide an \(L_2\) norm error estimate for LS finite element solution on graded meshes.
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Metadata
Title
Supercloseness of the mixed finite element method for the primary function on unstructured meshes and its applications
Author
JaEun Ku
Publication date
01-12-2014
Publisher
Springer Netherlands
Published in
BIT Numerical Mathematics / Issue 4/2014
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI
https://doi.org/10.1007/s10543-014-0494-0

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