Finite element formulations for moving boundaries, material interfaces, and postprocessing, with applications to heat transfer and consolidation in porous media

The research described here concerns finite element modeling of problems involving moving boundaries and different material types, together with postprocessing and superconvergence behavior. An example from geomechanics corresponding to underground coal gasification is included to demonstrate the moving grid and moving boundary technique. A new treatment for material interface elements is introduced as part of this formulation. In test calculations this treatment is shown to be superior to previous material averaging strategies. The postprocessing analysis and superconvergence theory is based on an entirely new approach which extensively uses Taylor series analysis and leads to some novel results in finite element modeling. These include new flux and stress postprocessing formulas, and new solution enhancement strategies. Some of these ideas are promising for treatment of other classes of problems such as those in reservoir engineering involving different material types and multiphase flow.