Higher order FEM for the obstacle problem of the p-Laplacian: A variational inequality approach

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Lothar Banz
  • Bishnu P. Lamichhane
  • Ernst P. Stephan

Research Organisations

External Research Organisations

  • University of Salzburg
  • University of Newcastle
View graph of relations

Details

Original languageEnglish
Pages (from-to)1639-1660
Number of pages22
JournalComputers and Mathematics with Applications
Volume76
Issue number7
Early online date21 Jul 2018
Publication statusPublished - 1 Oct 2018

Abstract

We consider higher order finite element discretizations of a nonlinear variational inequality formulation arising from an obstacle problem with the p-Laplacian differential operator for p∈(1,∞). We prove an a priori error estimate and convergence rates with respect to the mesh size h and in the polynomial degree q under assumed regularity. Moreover, we derive a general a posteriori error estimate which is valid for any uniformly bounded sequence of finite element functions. All our results contain the known results for the linear case of p=2. We present numerical results on the improved convergence rates of adaptive schemes (mesh size adaptivity with and without polynomial degree adaptation) for the singular case of p=1.5 and for the degenerated case of p=3.

Keywords

    A posteriori error estimate, A priori error estimate, hq-adaptive FEM, p-Laplacian obstacle problem

ASJC Scopus subject areas

Cite this

Higher order FEM for the obstacle problem of the p-Laplacian: A variational inequality approach. / Banz, Lothar; Lamichhane, Bishnu P.; Stephan, Ernst P.
In: Computers and Mathematics with Applications, Vol. 76, No. 7, 01.10.2018, p. 1639-1660.

Research output: Contribution to journal › Article › Research › peer review

Banz L, Lamichhane BP, Stephan EP. Higher order FEM for the obstacle problem of the p-Laplacian: A variational inequality approach. Computers and Mathematics with Applications. 2018 Oct 1;76(7):1639-1660. Epub 2018 Jul 21. doi: 10.1016/j.camwa.2018.07.016
Banz, Lothar ; Lamichhane, Bishnu P. ; Stephan, Ernst P. / Higher order FEM for the obstacle problem of the p-Laplacian : A variational inequality approach. In: Computers and Mathematics with Applications. 2018 ; Vol. 76, No. 7. pp. 1639-1660.
Download
@article{4148dfb6969f4d80a8f68a450f76e5c3,
title = "Higher order FEM for the obstacle problem of the p-Laplacian: A variational inequality approach",
abstract = "We consider higher order finite element discretizations of a nonlinear variational inequality formulation arising from an obstacle problem with the p-Laplacian differential operator for p∈(1,∞). We prove an a priori error estimate and convergence rates with respect to the mesh size h and in the polynomial degree q under assumed regularity. Moreover, we derive a general a posteriori error estimate which is valid for any uniformly bounded sequence of finite element functions. All our results contain the known results for the linear case of p=2. We present numerical results on the improved convergence rates of adaptive schemes (mesh size adaptivity with and without polynomial degree adaptation) for the singular case of p=1.5 and for the degenerated case of p=3.",
keywords = "A posteriori error estimate, A priori error estimate, hq-adaptive FEM, p-Laplacian obstacle problem",
author = "Lothar Banz and Lamichhane, {Bishnu P.} and Stephan, {Ernst P.}",
note = "Funding information: The visit of the third author to the University of Newcastle, Australia was partially supported by the priority research centre of the University of Newcastle for Computer-Assisted Research Mathematics and its Applications . He expresses his sincere thanks to Bishnu Lamichhane for his hospitality during the visit.",
year = "2018",
month = oct,
day = "1",
doi = "10.1016/j.camwa.2018.07.016",
language = "English",
volume = "76",
pages = "1639--1660",
journal = "Computers and Mathematics with Applications",
issn = "0898-1221",
publisher = "Elsevier Ltd.",
number = "7",

}

Download

TY - JOUR

T1 - Higher order FEM for the obstacle problem of the p-Laplacian

T2 - A variational inequality approach

AU - Banz, Lothar

AU - Lamichhane, Bishnu P.

AU - Stephan, Ernst P.

N1 - Funding information: The visit of the third author to the University of Newcastle, Australia was partially supported by the priority research centre of the University of Newcastle for Computer-Assisted Research Mathematics and its Applications . He expresses his sincere thanks to Bishnu Lamichhane for his hospitality during the visit.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We consider higher order finite element discretizations of a nonlinear variational inequality formulation arising from an obstacle problem with the p-Laplacian differential operator for p∈(1,∞). We prove an a priori error estimate and convergence rates with respect to the mesh size h and in the polynomial degree q under assumed regularity. Moreover, we derive a general a posteriori error estimate which is valid for any uniformly bounded sequence of finite element functions. All our results contain the known results for the linear case of p=2. We present numerical results on the improved convergence rates of adaptive schemes (mesh size adaptivity with and without polynomial degree adaptation) for the singular case of p=1.5 and for the degenerated case of p=3.

AB - We consider higher order finite element discretizations of a nonlinear variational inequality formulation arising from an obstacle problem with the p-Laplacian differential operator for p∈(1,∞). We prove an a priori error estimate and convergence rates with respect to the mesh size h and in the polynomial degree q under assumed regularity. Moreover, we derive a general a posteriori error estimate which is valid for any uniformly bounded sequence of finite element functions. All our results contain the known results for the linear case of p=2. We present numerical results on the improved convergence rates of adaptive schemes (mesh size adaptivity with and without polynomial degree adaptation) for the singular case of p=1.5 and for the degenerated case of p=3.

KW - A posteriori error estimate

KW - A priori error estimate

KW - hq-adaptive FEM

KW - p-Laplacian obstacle problem

UR - http://www.scopus.com/inward/record.url?scp=85050095261&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2018.07.016

DO - 10.1016/j.camwa.2018.07.016

M3 - Article

AN - SCOPUS:85050095261

VL - 76

SP - 1639

EP - 1660

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 7

ER -