A new adaptively deforming mixed variable finite element method will be used for a two-dimensional stability analysis of transient phase change processes in porous media with natural convection. Criteria developed from the computational work will be verified by experimental studies of formation and thawing of permafrost. Criteria developed from the study will be applicable to several types of moving front problems such as melting/freezing Stefon problems, growth of semiconductor crystals, welding of critical components, and transport of toxic contaminants in ground water.