A strategy to enforce the discrete minimax principle on finite element meshes

Low quality meshes in three-dimensional finite element diffusion simulations often violate the discrete Minimax principle. An indication of this shortcoming is the occurrence of negative concentrations. We present an a posteriori refinement algorithm to enforce the discrete Minimax principle by locally refining the mesh based on the last time-step. Two examples of diffusion simulations where negative concentrations could effectively be avoided by applying our refinement algorithm are presented. A final example is given to demonstrate the locality of the algorithm.