The space-continuous–discontinuous Galerkin method Original Research Article

The space-discontinuous finite element method for a scalar diffusion–convection-reaction problem is introduced and analyzed. In the solution method, the boundary conditions and the continuity of the solution at the element interfaces are forced in a weak sense. The convergence rate of the numerical solution is shown, however, to be the same as in the usual approach based on a continuous approximation. Finally, the benefits of the method with discontinuous–continuous approximation in h-adaptation of the finite element space are illustrated with the aid of numerical calculations.