In this paper we consider numerical schemes for multidimensional evolutionary convection–diffusion problems, where the approximation properties are uniform in the diffusion parameter. In order to obtain an efficient method, to provide good approximations with independence of the size of the diffusion parameter, we have developed a numerical method which combines a finite difference spatial disc...

In this paper, a parameter-uniform convergent numerical scheme is provided for solving singularly perturbed parabolic convection-diffusion differential equations with large delay. A priori bounds on the exact solution and its derivatives derived by asymptotic analysis of problem are provided.. The discretized Crank-Nicolson method uniform mesh in time direction fitted operator upwind finite dif...

This paper deals with singularly perturbed initial value problem for linear first-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first-order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous solution with respect to the perturbation paramet...

We consider the problem of triangulating an x-monotone polygon with a small number of different edge lengths using Steiner points. Given a parameter α, where 0 < α < 1, we shall present an algorithm for finding an almost uniform triangular mesh with 3π/8α2 + o(1/α2) different edge lengths such that every edge length is between l and (2 + √ 2α)l. Experiments demonstrate the effectiveness of this...

Due to their general and robust formulation deformable models offer a very appealing approach to 3D image segmentation. However there is a trade-off between model genericity, model accuracy and computational efficiency. In general, fully generic models require a uniform sampling of either the space or their mesh. The segmentation accuracy is thus a global parameter. Recovering small image featu...

Reliable and efficient residual-based a posteriori error estimates are established for the stabilised locking-free finite element methods for the Reissner-Mindlin plate model. The error is estimated by a computable error estimator from above and below up to multiplicative constants that do neither depend on the mesh-size nor on the plate’s thickness and are uniform for a wide range of stabilisa...

The weighted essentially non-oscillatory (WENO) methods are a popular high-order spatial discretization for hyperbolic partial differential equations. Typical treatments of WENO methods assume a uniform mesh. In this paper we give explicit formulas for the finite-volume, fifth-orderWENO (WENO5) method on non-uniform meshes in a way that is amenable to efficient implementation. We then compare t...