A hybridizable discontinuous Galerkin method for a class of fractional boundary value problems - Karaaslan, Mehmet Fatih; Celiker, Fatih; Kurulay, Muhammet (ELSEVIER SCIENCE BV, 2018)
In this paper, we present a hybridizable discontinuous Galerkin (HDG) method for solving a class of fractional boundary value problems involving Caputo derivatives. The HDG methods have the computational advantage of eliminating all internal degrees of freedom and the only globally coupled unknowns are those at the element interfaces. Furthermore, the global stiffness matrix is tridiagonal, symmetric, and positive definite. Internal degrees of freedom are recovered at an element-by-element postprocessing step. We carry out a series of numerical experiments to ascertain the performance of the proposed method. (C) 2017 Elsevier B.V. All rights reserved.
Keywords: Hybridizable discontinuous Galerkin methods; Fractional boundary value problems; Caputo derivative; DIFFERENTIAL-EQUATIONS; Mathematics