A numerical study on the finite element solution of singularly perturbed systems of reaction–diffusion problems

Finite Element Analysis of an Exponentially Graded Mesh for Singularly Perturbed Problems

“…Since for reaction-di usion problems there exist several numerical evidence that corroborate the claims made in this article (see [11][12][13]), in this section we present the results of numerical computations for the following model convection-di usion problem:…”

“…The mesh was constructed by optimizing certain upper bounds on the error (see [12] for details) and was used in the conjunction with the FEM for polynomials of degree ≥ 1. Since then, there has been no further analysis of the FEM on this mesh, even though numerical experiments illustrated its superiority over existing meshes, such as the Shishkin and Bakhvalov meshes, at least for reaction-di usion problems [13]. In the present article, we prove, for the rst time, the robustness of the ℎ version of the FEM on the exponential mesh as well as its optimal convergence rate in the energy norm.…”

Numerical Solution of Systems of Singularly Perturbed Differential Equations

“…Here we summarize the more general theoretical results for (2.8) from [20]. See also [40] for numerical results.…”

An almost third order finite difference scheme for singularly perturbed reaction–diffusion systems

“…In the context of FEM, up to our knowledge only the p and hp-version approximate the solution at an exponential rate of convergence. In [15] some numerical results showing the efficiency of this method were giving for the case of two equations. On the other hand, in [16] an arbitrary number of equations is considered, proving the convergence in the simpler case of equal diffusion parameters.…”