The boundary value problem for a singularly perturbed parabolic PDE with convection is considered on an interval in the case of the singularly perturbed Robin boundary condition; the highest space derivatives in the equation and in the boundary condition are multiplied by the perturbation parameter ε. In contrast to a Dirichlet boundary value problem, for the problem under consideration the err...

The boundary-value problem for a singularly perturbed parabolic PDE with convection is considered on an interval in the case of the singularly perturbed Robin boundary condition; the highest space derivatives in the equation and in the boundary condition are multiplied by the perturbation parameter ε. In contrast to the Dirichlet boundary-value problem, for the problem under consideration the e...

A procedure for the construction of robust, upper bounds for the error in the finite element approximation of singularly perturbed reaction diffusion problems was presented in [2] which entailed the solution of an infinite dimensional local boundary value problem. It is not possible to solve this problem exactly and this fact was recognised in the above work where it was indicated that the limi...

In this paper convergence on equidistributing meshes is investigated. Equidistributing meshes, or more generally approximate equidistributing meshes, are constructed through the well-known equidistribution principle and a so-called adaptation (or monitor) function which is defined based on estimates on interpolation error for polynomial preserving operators. Detailed convergence analysis is giv...