Analysis of Ciarlet–Raviart mixed finite element methods for solving damped Boussinesq equation

Maryam Parvizi; Amirreza Khodadadian; M. R. Eslahchi

doi:10.1016/j.cam.2020.112818

Analysis of Ciarlet–Raviart mixed finite element methods for solving damped Boussinesq equation

Maryam Parvizi^*, Amirreza Khodadadian, M. R. Eslahchi

^*Corresponding author for this work

Institute of Applied Mathematics

Research output: Contribution to journal › Article › Research › peer review

Abstract

In this paper, we consider the numerical solution of damped Boussinesq equation using Ciarlet–Raviart mixed finite element method. An implicit finite difference scheme is used for the time discretization. A priori error estimates are analyzed and stability analysis of the method is shown. We obtain an optimal error estimate in L² norm with quadratic or higher-order element, for both semi and fully discrete finite element approximations. Finally, numerical examples are given to verify the theoretical results.

Original language	English
Article number	112818
Journal	Journal of Computational and Applied Mathematics
Volume	379
E-pub ahead of print	6 Mar 2020
DOIs	https://doi.org/10.1016/j.cam.2020.112818
Publication status	Published - 1 Dec 2020

Keywords

Boussinesq equation
Ciarlet–Raviart method
Convergence
Finite difference method
Mixed finite element method
Stability

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2020.112818

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title = "Analysis of Ciarlet–Raviart mixed finite element methods for solving damped Boussinesq equation",

abstract = "In this paper, we consider the numerical solution of damped Boussinesq equation using Ciarlet–Raviart mixed finite element method. An implicit finite difference scheme is used for the time discretization. A priori error estimates are analyzed and stability analysis of the method is shown. We obtain an optimal error estimate in L2 norm with quadratic or higher-order element, for both semi and fully discrete finite element approximations. Finally, numerical examples are given to verify the theoretical results.",

keywords = "Boussinesq equation, Ciarlet–Raviart method, Convergence, Finite difference method, Mixed finite element method, Stability",

author = "Maryam Parvizi and Amirreza Khodadadian and Eslahchi, {M. R.}",

year = "2020",

month = dec,

day = "1",

doi = "10.1016/j.cam.2020.112818",

language = "English",

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T1 - Analysis of Ciarlet–Raviart mixed finite element methods for solving damped Boussinesq equation

AU - Parvizi, Maryam

AU - Khodadadian, Amirreza

AU - Eslahchi, M. R.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - In this paper, we consider the numerical solution of damped Boussinesq equation using Ciarlet–Raviart mixed finite element method. An implicit finite difference scheme is used for the time discretization. A priori error estimates are analyzed and stability analysis of the method is shown. We obtain an optimal error estimate in L2 norm with quadratic or higher-order element, for both semi and fully discrete finite element approximations. Finally, numerical examples are given to verify the theoretical results.

AB - In this paper, we consider the numerical solution of damped Boussinesq equation using Ciarlet–Raviart mixed finite element method. An implicit finite difference scheme is used for the time discretization. A priori error estimates are analyzed and stability analysis of the method is shown. We obtain an optimal error estimate in L2 norm with quadratic or higher-order element, for both semi and fully discrete finite element approximations. Finally, numerical examples are given to verify the theoretical results.

KW - Boussinesq equation

KW - Ciarlet–Raviart method

KW - Convergence

KW - Finite difference method

KW - Mixed finite element method

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=85083652850&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2020.112818

DO - 10.1016/j.cam.2020.112818

M3 - Article

AN - SCOPUS:85083652850

SN - 0377-0427

VL - 379

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 112818

ER -

Analysis of Ciarlet–Raviart mixed finite element methods for solving damped Boussinesq equation

Abstract

Keywords

ASJC Scopus subject areas

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