## Details

Original language | English |
---|---|

Pages (from-to) | 1639-1660 |

Number of pages | 22 |

Journal | Computers and Mathematics with Applications |

Volume | 76 |

Issue number | 7 |

Early online date | 21 Jul 2018 |

Publication status | Published - 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

- Mathematics(all)
**Modelling and Simulation**- Computer Science(all)
**Computational Theory and Mathematics**- Mathematics(all)
**Computational Mathematics**

## Cite this

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**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

*Computers and Mathematics with Applications*, vol. 76, no. 7, pp. 1639-1660. https://doi.org/10.1016/j.camwa.2018.07.016

*Computers and Mathematics with Applications*,

*76*(7), 1639-1660. https://doi.org/10.1016/j.camwa.2018.07.016

}

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 -