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

Abstract

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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.

How to cite

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Akrivis, 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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Citations in EuDML Documents

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  1. Konstantinos Chrysafinos, Sotirios P. Filopoulos, Theodosios K. Papathanasiou, Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
  2. Konstantinos Chrysafinos, Sotirios P. Filopoulos, Theodosios K. Papathanasiou, Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
  3. Konstantinos Chrysafinos, Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's
  4. Monika Balázsová, Miloslav Feistauer, On the stability of the ALE space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains
  5. Martin Balazovjech, Miloslav Feistauer, Jaromír Horáček, Martin Hadrava, Adam Kosík, Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

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