Publication result detail

Verification of Functional A Posteriori Error Estimates for Obstacle Problem in 1D

HARASIM, P.; VALDMAN, J.

Original Title

Verification of Functional A Posteriori Error Estimates for Obstacle Problem in 1D

English Title

Verification of Functional A Posteriori Error Estimates for Obstacle Problem in 1D

Type

Peer-reviewed article not indexed in WoS or Scopus

Original Abstract

We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.

English abstract

We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.

Keywords

obstacle problem, a posteriori error estimate, functional majorant, finite element method, variational inequalities, Uzawa algorithm

Key words in English

obstacle problem, a posteriori error estimate, functional majorant, finite element method, variational inequalities, Uzawa algorithm

Authors

HARASIM, P.; VALDMAN, J.

Released

20.11.2013

ISBN

0023-5954

Periodical

KYBERNETIKA

Volume

2013(49)

Number

5

State

Czech Republic

Pages from

738

Pages to

754

Pages count

17

BibTex

@article{BUT103637,
  author="Petr {Harasim} and Jan {Valdman}",
  title="Verification of Functional A Posteriori Error Estimates for Obstacle Problem in 1D",
  journal="KYBERNETIKA",
  year="2013",
  volume="2013(49)",
  number="5",
  pages="738--754",
  issn="0023-5954"
}