scholarly journals A posteriori error estimates for a fully discrete approximation of Sobolev equations

2019 ◽  
Vol 11 (1) ◽  
pp. 3-28
Author(s):  
Serge Nicaise ◽  
Fatiha Bekkouche
Keyword(s):  
Error Estimates ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Discrete Approximation ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Fully Discrete ◽  
Sobolev Equations ◽  
Fully Discrete Approximation

A Posteriori Error Estimates for Conservative Local Discontinuous GalerkinMethods for the Generalized Korteweg-de Vries Equation

2016 ◽  
Vol 20 (1) ◽  
pp. 250-278 ◽  
Author(s):  
Ohannes Karakashian ◽  
Yulong Xing
Keyword(s):  
Error Estimates ◽  
Vries Equation ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Fully Discrete ◽  
De Vries ◽  
Fully Discrete Approximation ◽  
Spatial Derivatives

AbstractWe construct and analyze conservative local discontinuous Galerkin (LDG) methods for the Generalized Korteweg-de-Vries equation. LDG methods are designed by writing the equation as a system and performing separate approximations to the spatial derivatives. The main focus is on the development of conservative methods which can preserve discrete versions of the first two invariants of the continuous solution, and a posteriori error estimates for a fully discrete approximation that is based on the idea of dispersive reconstruction. Numerical experiments are provided to verify the theoretical estimates.

scholarly journals A Priori and a Posteriori Error Estimates of a WOPSIP DG Method for the Heat Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yuping Zeng ◽  
Kunwen Wen ◽  
Fen Liang ◽  
Huijian Zhu
Keyword(s):  
Heat Equation ◽  
Error Estimates ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Fully Discrete ◽  
Backward Euler ◽  
Elliptic Reconstruction

We introduce and analyze a weakly overpenalized symmetric interior penalty method for solving the heat equation. We first provide optimal a priori error estimates in the energy norm for the fully discrete scheme with backward Euler time-stepping. In addition, we apply elliptic reconstruction techniques to derive a posteriori error estimators, which can be used to design adaptive algorithms. Finally, we present two numerical experiments to validate our theoretical analysis.

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