A quadrature finite element method for semilinear second‐order hyperbolic problems |
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| Authors: | K Mustapha H Mustapha |
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| Institution: | 1. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia;2. Reservoir Engineering Research Institute, (RERI), Palo Alto, California 94306 |
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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. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 |
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| Keywords: | Crank– Nicolson finite element method hyperbolic problems quadrature |
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