Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition

Hiroki Ishizaka

Applications of Mathematics (2024)

  • Volume: 69, Issue: 6, page 769-805
  • ISSN: 0862-7940

Abstract

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We present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptic equations. We do not impose the shape-regularity mesh condition in the analysis. Anisotropic meshes can be used for this purpose. The main contributions of this study include providing a new proof of the term consistency. This enables us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relationship between the Raviart-Thomas and Morley finite-element spaces. Our results indicate optimal convergence rates and imply that the modified Morley FEM may be effective for errors.

How to cite

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Ishizaka, Hiroki. "Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition." Applications of Mathematics 69.6 (2024): 769-805. <http://eudml.org/doc/299636>.

@article{Ishizaka2024,
abstract = {We present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptic equations. We do not impose the shape-regularity mesh condition in the analysis. Anisotropic meshes can be used for this purpose. The main contributions of this study include providing a new proof of the term consistency. This enables us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relationship between the Raviart-Thomas and Morley finite-element spaces. Our results indicate optimal convergence rates and imply that the modified Morley FEM may be effective for errors.},
author = {Ishizaka, Hiroki},
journal = {Applications of Mathematics},
keywords = {Morley finite element; anisotropic interpolation error; fourth-order elliptic problem},
language = {eng},
number = {6},
pages = {769-805},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition},
url = {http://eudml.org/doc/299636},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Ishizaka, Hiroki
TI - Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 6
SP - 769
EP - 805
AB - We present a precise anisotropic interpolation error estimate for the Morley finite element method (FEM) and apply it to fourth-order elliptic equations. We do not impose the shape-regularity mesh condition in the analysis. Anisotropic meshes can be used for this purpose. The main contributions of this study include providing a new proof of the term consistency. This enables us to obtain an anisotropic consistency error estimate. The core idea of the proof involves using the relationship between the Raviart-Thomas and Morley finite-element spaces. Our results indicate optimal convergence rates and imply that the modified Morley FEM may be effective for errors.
LA - eng
KW - Morley finite element; anisotropic interpolation error; fourth-order elliptic problem
UR - http://eudml.org/doc/299636
ER -

References

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