Singularly perturbed reaction-diffusion problem with a boundary turning point

Parameter uniform numerical methods for singularly perturbed reaction diffusion problems have been examined extensively in the literature. By using layer adapted meshes of Bahkvalov or Shishkin type, it is now well established that one can achieve second order (or almost second order in the case of the simpler Shishkin meshes) parameter uniform convergence globally in the pointwise maximum norm. Note that, in proving such results, it is often assumed that the coefficient of the reactive term is strictly positive throughout the domain. In this paper, we examine a problem where the reaction coefficient is zero on parts of the boundary.