# Galerkin time-stepping methods for nonlinear parabolic equations

Georgios Akrivis; Charalambos Makridakis

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 38.2 (2010): 261-289. <http://eudml.org/doc/194214>.

@article{Akrivis2010,

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},

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

language = {eng},

month = {3},

number = {2},

pages = {261-289},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/194214},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Akrivis, Georgios

AU - Makridakis, Charalambos

TI - Galerkin time-stepping methods for nonlinear parabolic equations

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

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; nonlinear parabolic equations; space-time finite element; time discretization; numerical examples

UR - http://eudml.org/doc/194214

ER -

## References

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- Konstantinos Chrysafinos, Sotirios P. Filopoulos, Theodosios K. Papathanasiou, Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
- Konstantinos Chrysafinos, Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's
- Martin Balazovjech, Miloslav Feistauer, On the stability of the ALE space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains

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