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 ≥ 2 is an integer, to approximating the space derivatives. The stability together with the error estimates of the constructed technique are established in W 2 1 (Ω) -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. [ABSTRACT FROM AUTHOR]