Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems Academic Article uri icon

abstract

  • © 2015, Springer-Verlag Berlin Heidelberg. Residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polyhedral domains. Standard finite element approximations are considered. The error constants are independent of the diameters of mesh elements and the small perturbation parameter. In our analysis, we employ sharp bounds on the Green’s function of the linearized differential operator. Numerical results are presented that support our theoretical findings.

author list (cited authors)

  • Demlow, A., & Kopteva, N.

citation count

  • 17

publication date

  • August 2015