Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type

Liping Liu; Michal Křížek; Pekka Neittaanmäki

Applications of Mathematics (1996)

  • Volume: 41, Issue: 6, page 467-478
  • ISSN: 0862-7940

Abstract

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A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree k ≥ 1 we prove the optimal rates of convergence 𝒪 ( h k ) in the H 1 -norm and 𝒪 ( h k + 1 ) in the L 2 -norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account.

How to cite

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Liu, Liping, Křížek, Michal, and Neittaanmäki, Pekka. "Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type." Applications of Mathematics 41.6 (1996): 467-478. <http://eudml.org/doc/32962>.

@article{Liu1996,
abstract = {A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree $k\ge 1$ we prove the optimal rates of convergence $\mathcal \{O\}(h^k)$ in the $H^1$-norm and $\mathcal \{O\}(h^\{k+1\})$ in the $L^2$-norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account.},
author = {Liu, Liping, Křížek, Michal, Neittaanmäki, Pekka},
journal = {Applications of Mathematics},
keywords = {nonlinear boundary value problem; finite elements; rate of convergence; anisotropic heat conduction; nonlinear boundary value problem; finite elements; rate of convergence; anisotropic heat conduction},
language = {eng},
number = {6},
pages = {467-478},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type},
url = {http://eudml.org/doc/32962},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Liu, Liping
AU - Křížek, Michal
AU - Neittaanmäki, Pekka
TI - Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 6
SP - 467
EP - 478
AB - A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree $k\ge 1$ we prove the optimal rates of convergence $\mathcal {O}(h^k)$ in the $H^1$-norm and $\mathcal {O}(h^{k+1})$ in the $L^2$-norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account.
LA - eng
KW - nonlinear boundary value problem; finite elements; rate of convergence; anisotropic heat conduction; nonlinear boundary value problem; finite elements; rate of convergence; anisotropic heat conduction
UR - http://eudml.org/doc/32962
ER -

References

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