It is shown that the interelement discontinuities in a discontinuous Galerkin finite element approximation are subordinate to the error measured in the broken H1-seminorm. One consequence is that the DG-norm of the error is equivalent to the broken energy seminorm. Computable a posteriori error bounds are obtained for the error measured in both the DG-normâ€¦ (More)

Algorithms are presented that enable the element matrices for the standard finite element space, consisting of continuous piecewise polynomials of degree n on simplicial elements in R, to be computed in optimal complexity O(n). The algorithms (i) take account of numerical quadrature; (ii) are applicable to non-linear problems; and, (iii) do not rely onâ€¦ (More)

We study the dispersion and dissipation of the numerical scheme obtained by taking a weighted averaging of the consistent (finite element) mass matrix and lumped (spectral element) mass matrix for the small wavenumber limit. We find and prove that for the optimum blending the resulting scheme (a) provides 2p+4 order accuracy for p-th order method (twoâ€¦ (More)

We derive computable a posteriori error estimates for the lowest order nonconforming Crouzeixâ€“Raviart element applied to the approximation of incompressible Stokes flow. The estimator provides an explicit upper bound that is free of any unknown constants, provided that a reasonable lower bound for the inf-sup constant of the underlying problem is available.â€¦ (More)