A parameter robust Petrov-Galerkin scheme for advection-diffusion-reaction equations (Q621786)

This paper deals with a singularly perturbed differential equation \[ -(\varepsilon(x) u')'+ a(x) u'+ b(x) u= f(x),\quad x\in (0,1)\setminus\{d_i\}^m_{i=1}, \] where the variable diffusion coefficient \(\varepsilon\) and the other data \(a\), \(b\), \(f\), can be discontinuous at the points \(d_i\in (0,1)\). A parameter-uniform numerical method for such problem is constructed. The authors use a combination of a fitted finite difference operator and a fitted layer-adapted mesh to simplify the analysis of a high-order parameter-uniform globally convergent numerical method. Four numerical examples are given.