An algebraic approach to the design of multidimensional
high-resolution schemes is introduced and elucidated in
the finite element context. A centered space discretization
of unstable convective terms is rendered local extremum
diminishing by a conservative elimination of negative
off-diagonal coefficients from the discrete transport operator.
This modification leads to an upwind-biased low-order scheme
which is nonoscillatory but overly diffusive. In order to reduce
the incurred error, a limited amount of compensating antidiffusion
is added in regions where the solution is sufficiently smooth.
A node-oriented flux limiter of TVD type is designed so as to
control the ratio of upstream and downstream edge contibutions
to each node. Nonlinear algebraic systems are solved by an
iterative defect correction scheme preconditioned by the
low-order evolution operator which enjoys the M-matrix
property. The diffusive and antidiffusive terms are represented
as a sum of antisymmetric internodal fluxes which are
constructed edge-by-edge and inserted into the global
vectors. The new methodology is applied to the equations of
the k-epsilon turbulence model and relevant implementation
aspects are addressed. Numerical results are presented for
the three-dimensional incompressible flow over a backward
facing step.