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Goran Radojev

Publications and source records attributed to Goran Radojev.

6 recordsLinked to original sources
arXiv2024

Maximum-norm a posteriori error bounds for parabolic equations discretised by the extrapolated Euler method in time and FEM in space

A class of linear parabolic equations is considered. We derive a framework for the a posteriori error analysis of time discretisations by Richardson extrapolation of arbitrary order combined with finite element discretisations in space. We use the idea of elliptic reconstructions and certain bounds for the Green's function of the parabolic operator. The crucial point in the analysis is the design of suitable polynomial reconstructions in time from approximations that are given only in the mesh points.

math.NA↗
arXiv2023

Maximum-norm a posteriori error bounds for an extrapolated upwind scheme applied to a singularly perturbed convection-diffusion problem

Richardson extrapolation is applied to a simple first-order upwind difference scheme for the approximation of solutions of singularly perturbed convection-diffusion problems in one dimension. Robust a posteriori error bounds are derived for the proposed method on arbitrary meshes. It is shown that the resulting error estimator can be used to stear an adaptive mesh algorithm that generates meshes resolving layers and singularities. Numerical results are presented that illustrate the theoretical findings.

math.NA↗
arXiv2023

A unified approach to maximum-norm a posteriori error estimation for second-order time discretisations of parabolic equations

A class of linear parabolic equations are considered. We derive a common framework for the a posteriori error analysis of certain second-order time discretisations combined with finite element discretisations in space. In particular we study the Crank-Nicolson method, the extrapolated Euler method, the backward differentiation formula of order 2 (BDF-2), the Lobatto IIIC method and a two-stage SDIRK method. We use the idea of elliptic reconstructions and certain bounds for the Green's function of the parabolic operator.

math.NA↗
arXiv2020

Superconvergence analysis of FEM and SDFEM on graded meshes for a problem with characteristic layers

We consider a singularly perturbed convection-diffusion with exponential and characteristic boundary layers. The problem is numerically solved by the FEM and SDFEM method with bilinear elements on a graded mesh. For the FEM we prove almost uniform convergence and superconvergence. The use of graded mesh allows for the SDFEM to prove almost uniform esimates in the SD norm, which is not possible for Shishkin type meshes.

math.NA↗