| Abstract: | The objective of the research presented here was to develop a generic adaptive computational method for porous media evolution problems that involve coupled heat flow, fluid flow and species transport processes with sharply defined phase-change interfaces. In this paper we examine the general least squares variational approach and develop the conceptual framework for a rate least squares variational formulation of a continuously deforming mixed variable finite element method for solving highly non-linear time-dependent partial differential equations. In Part II of this paper1 we extend the formulation given here for a single evolution equation to a system of coupled evolution equations. In Part III2 we discuss in detail the numerical procedures that were implemented in a computer program and present several numerical examples that demonstrate the performance of this computational method. |
