Finite element approximations with quadrature for second‐order hyperbolic equations
Copyright policy )Finite element approximations with quadrature for second‐order hyperbolic equations
AbstractIn this article, the effect of numerical quadrature on the finite element Galerkin approximations to the solution of hyperbolic equations has been studied. Both semidiscrete and fully discrete schemes are analyzed and optimal estimates are derived in the L∞(H1), L∞(L2) norms, whereas quasi‐optimal estimate is derived in the L∞(L∞) norm using energy methods. The analysis in the present paper improves upon the earlier results of Baker and Dougalis [SIAM J Numer Anal 13 (1976), pp 577–598] under the minimum smoothness assumptions of Rauch [SIAM J Numer Anal 22 (1985), pp 245–249] for a purely second‐order hyperbolic equation with quadrature. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 537–559, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10022
Method of lines for initial value and initial-boundary value problems involving PDEs, Error bounds for initial value and initial-boundary value problems involving PDEs, Numerical integration, finite element method, second-order hyperbolic equation, semidiscretization, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Initial value problems for second-order hyperbolic equations, error bounds, Galerkin method, numerical quadrature
Method of lines for initial value and initial-boundary value problems involving PDEs, Error bounds for initial value and initial-boundary value problems involving PDEs, Numerical integration, finite element method, second-order hyperbolic equation, semidiscretization, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Initial value problems for second-order hyperbolic equations, error bounds, Galerkin method, numerical quadrature
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