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Biquadratic finite volume element method based on optimal stress points for second order hyperbolic equations
Author(s) -
Yu Changhua,
Li Yonghai
Publication year - 2013
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.21724
Subject(s) - superconvergence , mathematics , finite element method , hyperbolic partial differential equation , convergence (economics) , order (exchange) , partial differential equation , finite volume method , stress (linguistics) , mathematical analysis , mechanics , linguistics , philosophy , physics , finance , economics , economic growth , thermodynamics
Based on optimal stress points, we develop a full discrete finite volume element scheme for second order hyperbolic equations using the biquadratic elements. The optimal order error estimates in L ∞ ( H 1 ), L ∞ ( L 2 ) norms are derived, in addition, the superconvergence of numerical gradients at optimal stress points is also discussed. Numerical results confirm the theoretical order of convergence. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013