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. Martin Balazovjech, Miloslav Feistauer, Jaromír Horáček, Martin Hadrava, Adam Kosík, Space-time discontinuous Galerkin method for the solution of fluid-structure interaction
  4. Martin Balazovjech, Miloslav Feistauer, On the stability of the ALE space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains
  5. Konstantinos Chrysafinos, Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's

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