Approximate solution of the Bagley-Torvik equation by hybridizable discontinuous Galerkin methods - Karaaslan, Mehmet Fatih; Celiker, Fatih; Kurulay, Muhammet (ELSEVIER SCIENCE INC, 2016)
In this paper, we introduce a hybridizable discontinuous Galerkin method for numerically solving a boundary value problem associated with the Bagley-Torvik equation that arises in the study of the motion of a plate immersed in a Newtonian fluid. One of the main features of these methods is that they are efficiently implementable since it is possible to eliminate all internal degrees of freedom and obtain a global linear system that only involves unknowns at the element interfaces. We display the results of a series of numerical experiments to ascertain the performance of the method. (C) 2016 Elsevier Inc. All rights reserved.
Keywords: Hybridizable discontinuous Galerkin methods; Bagley-Torvik equation; Fractional derivative; Fractional calculus; WAVELET OPERATIONAL MATRIX; BOUNDARY-VALUE-PROBLEMS; NUMERICAL-SOLUTION; HDG METHODS; ORDER; Mathematics