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

✍ Scribed by K. Mustapha; H. Mustapha

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 178 KB
• Volume: 24
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.20262

✦ Synopsis

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. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008