The two-level local projection stabilization is considered as a onelevel approach in which the enrichments on each element are piecewise polynomial functions. The dimension of the enrichment space can be significantly reduced without losing the convergence order. For example, using continuous piecewise polynomials of degree r ≥ 1, only one function per cell is needed as enrichment instead of r ...

A system ofM(≥ 2) coupled singularly perturbed linear reaction-diffusion equations is considered on the unit square. Under certain hypotheses on the coupling, a maximum principle is established for the differential operator. The relationship between compatibility conditions at the corners of the square and the smoothness of the solution on the closed domain is fully described. A decomposition o...

In this paper we study the discrete approximation of a Dirichlet problem on an interval for a singularly perturbed parabolic PDE. The highest derivative in the equation is multiplied by an arbitrarily small parameter ε. If the parameter vanishes, the parabolic equation degenerates to a first-order equation, in which only the time derivative remains. For small values of the parameter, boundary l...

in this paper, a higher order continuum model is presented based on the cosserat continuum theory in 3d numerical simulation of shear band localization. as the classical continuum models suffer from the pathological mesh-dependence in strain softening models, the governing equations are regularized by adding the rotational degrees-of-freedom to conventional degrees-of-freedom. the fundamental r...

We consider grid approximations of a boundary value problem for the boundary layer equations modeling flow along a flat plate in a region excluding a neighbourhood of the leading edge. The problem is singularly perturbed with the perturbation parameter ε = 1/Re multiplying the highest derivative. Here the parameter ε takes any values from the half-interval (0,1], and Re is the Reynolds number. ...

Normal Doo-Sabin subdivision surfaces are based on uniform quadratic B-splines. This makes it somewhat more difficult to produce an object with sharp creases or corners using normal Doo-Sabin subdivision. Non-Uniform Subdivision Surfaces on the other hand, allow for the possibility of creating an object that will keep specific points sharp based on the knot intervals that a particular edge is a...