A quadrature finite element method for semilinear second-order hyperbolic problems

K. Mustapha; H. Mustapha

doi:10.1002/num.20262

A quadrature finite element method for semilinear second-order hyperbolic problems

K. Mustapha^*
, H. Mustapha

^*Corresponding author for this work

Department of Mathematics

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

2 Scopus citations

Abstract

In this work we propose and analyze a fully discrete modified Crank-Nicolson finite element (CNFE) method with quadrature for solving semilinear second-order hyperbolic initial-boundary value problems. We prove optimal-order convergence in both time and space for the quadrature-modified CNFE scheme that does not require nonlinear algebraic solvers. Finally, we demonstrate numerically the order of convergence of our scheme for some test problems.

Original language	English
Pages (from-to)	350-367
Number of pages	18
Journal	Numerical Methods for Partial Differential Equations
Volume	24
Issue number	2
DOIs	https://doi.org/10.1002/num.20262
State	Published - Mar 2008

Keywords

Crank-Nicolson
Finite element method
Hyperbolic problems
Quadrature

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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abstract = "In this work we propose and analyze a fully discrete modified Crank-Nicolson finite element (CNFE) method with quadrature for solving semilinear second-order hyperbolic initial-boundary value problems. We prove optimal-order convergence in both time and space for the quadrature-modified CNFE scheme that does not require nonlinear algebraic solvers. Finally, we demonstrate numerically the order of convergence of our scheme for some test problems.",

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AU - Mustapha, H.

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N2 - In this work we propose and analyze a fully discrete modified Crank-Nicolson finite element (CNFE) method with quadrature for solving semilinear second-order hyperbolic initial-boundary value problems. We prove optimal-order convergence in both time and space for the quadrature-modified CNFE scheme that does not require nonlinear algebraic solvers. Finally, we demonstrate numerically the order of convergence of our scheme for some test problems.

AB - In this work we propose and analyze a fully discrete modified Crank-Nicolson finite element (CNFE) method with quadrature for solving semilinear second-order hyperbolic initial-boundary value problems. We prove optimal-order convergence in both time and space for the quadrature-modified CNFE scheme that does not require nonlinear algebraic solvers. Finally, we demonstrate numerically the order of convergence of our scheme for some test problems.

KW - Crank-Nicolson

KW - Finite element method

KW - Hyperbolic problems

KW - Quadrature

UR - https://www.scopus.com/pages/publications/40749162719

U2 - 10.1002/num.20262

DO - 10.1002/num.20262

M3 - Article

AN - SCOPUS:40749162719

SN - 0749-159X

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JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 2

ER -

A quadrature finite element method for semilinear second-order hyperbolic problems

Abstract

Keywords

ASJC Scopus subject areas

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