A high-order combined finite element/interpolation approach for multidimensional nonlinear generalized Benjamin-Bona-Mahony-Burgers equation

A high-order combined finite element/interpolation approach is developed for solving a multidimensional nonlinear generalized Benjamin-Bona-Mahony-Burgers equation subjected to suitable initial and boundary conditions. In the proposed high-order scheme we approximate the time derivative with piecewise polynomial interpolation of second-order and use the finite element discretization of piecewise polynomials of degree q and q + 1, where q & GE; 2 is an integer, to approximating the space derivatives. The stability together with the error estimates of the constructed technique are established in W21 (& OHM;)-norm. The analysis suggests that the developed numerical scheme is unconditionally stable, temporal second-order accurate and convergence in space with order q. Furthermore, the new procedure is faster and more efficient than a broad range of numerical methods discussed in the literature for the given initial-boundary value problem. A wide set of examples are performed to confirming the theoretical studies.& COPY; 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.