Explorations and Expectations of Equidistribution Adaptations for Nonlinear Quenching Problems (Advances in Applied Mathematics and Mechanics, 2021)
Finite difference computations that involve spatial adaptation commonly employ anequidistribution principle. In these cases, a new mesh is constructed such that agiven monitor function is equidistributed in some sense. Typical choices of themonitor function involve the solution or one of its many derivatives. This straightforwardconcept has proven to be extremely effective and practical. However, selections of coremonitoring functions are often challengingand crucial to the computational success. This paper concerns six differentdesigns of the monitoring function that targets a highly nonlinear partialdifferential equation that exhibits both quenching-type and degeneracy singularities.While the first four monitoring strategies are within the so-calledprimitive regime, the rest belong to a later category of themodified type, which requires the priori knowledge of certainimportant quenching solution characteristics. Simulated examples are givento illustrate our study and conclusions.