Search

Abstract An H 1 -Galerkin mixed finite element method (MFEM) is developed for the Benjamin–Bona–Mahony (BBM) equation with the bilinear element and zero order Raviart–Thomas element pair (Q 11 ∕ Q 10 × Q 01). Then based on the special interpolation properties of the above two elements and the mean-value technique, the supercloseness and superconvergence results of order O (h 2) for the semi-discrete scheme and of order O (h 2 + (Δ t) 2) for the Crank–Nicolson fully-discrete scheme are deduced for the original variable u in H 1 -norm and the flux p → in H (d i v , Ω) -norm, respectively. Finally, a numerical example is carried out to demonstrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

A Galerkin finite element method (FEM) is developed for nonlinear Poisson–Nernst–Planck (PNP) equations. Based on the combination technique of the element's interpolation and Ritz projection together with the special mean value approach, the superclose and superconvergence estimates with order O (h 2) are derived under weaker regularity requirements of the exact solution. Some numerical results are provided to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]