Picard iteration convergence analysis in a Galerkin finite element approximation of the one-dimensional shallow water equations

1993 ◽  
Vol 9 (1) ◽  
pp. 77-92 ◽  
Author(s):  
B. Cathers ◽  
B. A. O'Connor
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Convergence Analysis ◽  
Shallow Water Equations ◽  
Finite Element Approximation ◽  
Picard Iteration ◽  
Element Approximation ◽  
Galerkin Finite Element ◽  
One Dimensional ◽  
The One

Well-Balanced Second-Order Finite Element Approximation of the Shallow Water Equations with Friction

2018 ◽  
Vol 40 (6) ◽  
pp. A3873-A3901 ◽  
Author(s):  
Jean-Luc Guermond ◽  
Manuel Quezada de Luna ◽  
Bojan Popov ◽  
Christopher E. Kees ◽  
Matthew W. Farthing
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Element Approximation ◽  
Second Order ◽  
Element Approximation

DISCRETE COMPACTNESS FOR p AND hp 2D EDGE FINITE ELEMENTS

2003 ◽  
Vol 13 (11) ◽  
pp. 1673-1687 ◽  
Author(s):  
DANIELE BOFFI ◽  
LESZEK DEMKOWICZ ◽  
MARTIN COSTABEL
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Stability Estimate ◽  
Element Approximation ◽  
Dimensional Model ◽  
Compactness Property ◽  
One Dimensional ◽  
Discrete Compactness

In this paper we discuss the hp edge finite element approximation of the Maxwell cavity eigenproblem. We address the main arguments for the proof of the discrete compactness property. The proof is based on a conjectured L2 stability estimate for the involved polynomial spaces which has been verified numerically for p≤15 and illustrated with the corresponding one dimensional model problem.

Numerical Analysis for a Nonlocal Parabolic Problem

2016 ◽  
Vol 6 (4) ◽  
pp. 434-447 ◽  
Author(s):  
M. Mbehou ◽  
R. Maritz ◽  
P.M.D. Tchepmo
Keyword(s):  
Finite Element ◽  
Parabolic Problem ◽  
Reaction Diffusion ◽  
Finite Element Approximation ◽  
Reaction Diffusion Equation ◽  
Element Approximation ◽  
Galerkin Finite Element ◽  
Fully Discrete ◽  
Nonlinear Reaction Diffusion Equation ◽  
Nonlinear Parabolic

AbstractThis article is devoted to the study of the finite element approximation for a nonlocal nonlinear parabolic problem. Using a linearised Crank-Nicolson Galerkin finite element method for a nonlinear reaction-diffusion equation, we establish the convergence and error bound for the fully discrete scheme. Moreover, important results on exponential decay and vanishing of the solutions in finite time are presented. Finally, some numerical simulations are presented to illustrate our theoretical analysis.

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