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A quadrature finite element method for semilinear second‐order hyperbolic problems
Author(s) -
Mustapha K.,
Mustapha H.
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20262
Subject(s) - mathematics , quadrature (astronomy) , finite element method , boundary value problem , mathematical analysis , hyperbolic partial differential equation , convergence (economics) , nonlinear system , algebraic number , partial differential equation , physics , quantum mechanics , economic growth , electrical engineering , economics , thermodynamics , engineering
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. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008