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Advanced Numerical Methods in the Mathematical Sciences

Alan Demlow, Texas A&M University
A Posteriori Error Estimation and Adaptivity in the Maximum Norm


  • Alan Demlow, Texas A&M University
  • Natalia Kopteva, University of Limerick (Ireland)


In this talk, I will discuss recent progress in constructing adaptive algorithms for controlling errors in the maximum norm. The main focus will be the construction of robust a posteriori error estimators for singularly perturbed elliptic reaction-diffusion problems. I will also discuss the sharpness of logarithmic factors that typically arise in maximum norm a posteriori estimates. In particular, we show that standard estimators for controlling maximum errors efficiently and reliably control the error in a modified bounded mean oscillation (BMO) norm with no logarithmic factors present.