A mixed‐variable continuously deforming finite element method for parabolic evolution problems. Part I: The variational formulation for a single evolution equation
Ifiyenia Kececioglu, Boris E. Rubinsky · International Journal for Numerical Methods in Engineering · 1989
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.