# Galerkin time-stepping methods for nonlinear parabolic equations

Georgios Akrivis; Charalambos Makridakis

- Volume: 38, Issue: 2, page 261-289
- ISSN: 0764-583X

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topAkrivis, Georgios, and Makridakis, Charalambos. "Galerkin time-stepping methods for nonlinear parabolic equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.2 (2004): 261-289. <http://eudml.org/doc/245171>.

@article{Akrivis2004,

abstract = {We consider discontinuous as well as continuous Galerkin methods for the time discretization of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity a priori error estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation.},

author = {Akrivis, Georgios, Makridakis, Charalambos},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {nonlinear parabolic equations; local Lipschitz condition; continuous and discontinuous Galerkin methods; a priori error analysis; monotone operators; discontinuous and continuous Galerkin methods; space-time finite element; time discretization; numerical examples},

language = {eng},

number = {2},

pages = {261-289},

publisher = {EDP-Sciences},

title = {Galerkin time-stepping methods for nonlinear parabolic equations},

url = {http://eudml.org/doc/245171},

volume = {38},

year = {2004},

}

TY - JOUR

AU - Akrivis, Georgios

AU - Makridakis, Charalambos

TI - Galerkin time-stepping methods for nonlinear parabolic equations

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2004

PB - EDP-Sciences

VL - 38

IS - 2

SP - 261

EP - 289

AB - We consider discontinuous as well as continuous Galerkin methods for the time discretization of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity a priori error estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation.

LA - eng

KW - nonlinear parabolic equations; local Lipschitz condition; continuous and discontinuous Galerkin methods; a priori error analysis; monotone operators; discontinuous and continuous Galerkin methods; space-time finite element; time discretization; numerical examples

UR - http://eudml.org/doc/245171

ER -

## References

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- [14] O. Karakashian and C. Makridakis, Convergence of a continuous Galerkin method with mesh modification for nonlinear wave equations. Math. Comp. (to appear). Zbl1057.65066MR2085403
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