A Robust DPG Method for Singularly Perturbed Reaction-Diffusion Problems

Mesh Refinement Strategies for Solving Singularly Perturbed Reaction-Diffusion Problems

we consider the numerical approximation of a singularly perturbed reaction-diffusion problem over a square. Two different. approaches are compared namely: adaptive isotropic mesh refinement and anisotropic mesh refinement. Thus, we compare the h-refinement and the Shishkin mesh approaches numerically with PLTMG software [l]. It is shown how isotropic elements lead to over-refinement. and how an...

Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems

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...

A robust grid equidistribution method for a one-dimensional singularly perturbed semilinear reaction-diffusion problem∗

The numerical solution of a singularly perturbed semilinear reaction-diffusion two-point boundary value problem is addressed. The method considered is adaptive movement of a fixed number (N +1) of mesh points by equidistribution of a monitor function that uses discrete second-order derivatives. We extend the analysis by Kopteva & Stynes (2001) to a new equation and a more intricate monitor func...

A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems

Consider the singularly perturbed linear reaction-diffusion problem −ε2Δu+ bu = f in Ω ⊂ Rd, u = 0 on ∂Ω, where d ≥ 1, the domain Ω is bounded with (when d ≥ 2) Lipschitzcontinuous boundary ∂Ω, and the parameter ε satisfies 0 < ε 1. It is argued that for this type of problem, the standard energy norm v → [ε|v|1+‖v‖0] is too weak a norm to measure adequately the errors in solutions computed by f...

Robust DPG Method for Convection-Dominated Diffusion Problems