article

Quasi-norm a priori and a posteriori error estimates for the nonconforming approximation of p-Laplacian

Authors:

Ningning YanAuthors Info & Claims

Numerische Mathematik, Volume 89, Issue 2

Pages 341 - 378

https://doi.org/10.1007/PL00005470

Published: 01 August 2001 Publication History

Abstract

In this paper, we derive quasi-norm a priori and a posteriori error estimates for the Crouzeix-Raviart type finite element approximation of the p-Laplacian. Sharper a priori upper error bounds are obtained. For instance, for sufficiently regular solutions we prove optimal a priori error bounds on the discretization error in an energy norm when $1 < p \leq 2$. We also show that the new a posteriori error estimates provide improved upper and lower bounds on the discretization error. For sufficiently regular solutions, the a posteriori error estimates are further shown to be equivalent on the discretization error in a quasi-norm.

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Cited By

del Teso FLindgren E(2021)A Finite Difference Method for the Variational p-LaplacianJournal of Scientific Computing10.1007/s10915-021-01745-z90:1Online publication date: 31-Dec-2021
https://dl.acm.org/doi/10.1007/s10915-021-01745-z
Pietro DDroniou JHarnist A(2021)Improved error estimates for Hybrid High-Order discretizations of Leray–Lions problemsCalcolo: a quarterly on numerical analysis and theory of computation10.1007/s10092-021-00410-z58:2Online publication date: 1-Jun-2021
https://dl.acm.org/doi/10.1007/s10092-021-00410-z
Zhou GFeng C(2013)The steepest descent algorithm without line search for p-LaplacianApplied Mathematics and Computation10.1016/j.amc.2013.07.096224(36-45)Online publication date: 1-Nov-2013
https://dl.acm.org/doi/10.1016/j.amc.2013.07.096
Show More Cited By

Index Terms

Quasi-norm a priori and a posteriori error estimates for the nonconforming approximation of p-Laplacian
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Numerische Mathematik

Numerische Mathematik Volume 89, Issue 2

August 2001

205 pages

ISSN:0029-599X

Issue’s Table of Contents

Copyright © Copyright © 2001 Springer-Verlag Berlin Heidelberg.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 August 2001

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Cited By

del Teso FLindgren E(2021)A Finite Difference Method for the Variational p-LaplacianJournal of Scientific Computing10.1007/s10915-021-01745-z90:1Online publication date: 31-Dec-2021
https://dl.acm.org/doi/10.1007/s10915-021-01745-z
Pietro DDroniou JHarnist A(2021)Improved error estimates for Hybrid High-Order discretizations of Leray–Lions problemsCalcolo: a quarterly on numerical analysis and theory of computation10.1007/s10092-021-00410-z58:2Online publication date: 1-Jun-2021
https://dl.acm.org/doi/10.1007/s10092-021-00410-z
Zhou GFeng C(2013)The steepest descent algorithm without line search for p-LaplacianApplied Mathematics and Computation10.1016/j.amc.2013.07.096224(36-45)Online publication date: 1-Nov-2013
https://dl.acm.org/doi/10.1016/j.amc.2013.07.096
Carstensen CKlose R(2003)A Posteriori Finite Element Error Control for the P-Laplace ProblemSIAM Journal on Scientific Computing10.1137/S106482750241661725:3(792-814)Online publication date: 1-Jan-2003
https://dl.acm.org/doi/10.1137/S1064827502416617
Liu WYan N(2003)A posteriori error estimates for control problems governed by nonlinear elliptic equationsApplied Numerical Mathematics10.1016/S0168-9274(03)00054-047:2(173-187)Online publication date: 1-Nov-2003
https://dl.acm.org/doi/10.1016/S0168-9274%2803%2900054-0
Liu WYan N(2002)Some a Posteriori Error Estimators for p-Laplacian Based on Residual Estimation or Gradient RecoveryJournal of Scientific Computing10.1023/A:101324642470716:4(435-477)Online publication date: 19-Feb-2002
https://dl.acm.org/doi/10.1023/A%3A1013246424707

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