P-VERSION LEAST-SQUARES FINITE-ELEMENT FORMULATION FOR AXISYMMETRICALHEAT-CONDUCTION WITH TEMPERATURE-DEPENDENT THERMAL-CONDUCTIVITIES

This paper presents a p-version least squares formulation for axisymme tric heat conduction with temperatures dependent thermal conductivites . The two-dimensional p-version hierarchical approximation functions a nd the corresponding nodal variable operators required in the element approximation are derived by first constructing the one-dimensional p- version hierarchical approximation functions and the corresponding nod al variable operators in the natural coordinate directions xi and eta for three node equivalent configurations that correspond to (p(xi) + 1 ) and (p(eta) + 1) equally spaced Lagrange nodal configurations, and t hen taking their products. The Fourier heat conduction equation in a c ylindrical coordinate system is recast into an equivalent system of co upled first-order differential equations through the use of auxiliary variables (fluxes q(r) and q(z)) for which p-version least squares fin ite element formulation (LSFEF) is constructed using equal order C0, p -version hierarchical approximation functions for both primary (temper ature T) and secondary variables (fluxes q(r) and q(z)). The resulting system of nonlinear algebraic equations is solved using Newton's meth od optimized with a line search. This procedure yields a symmetric Hes sian matrix which possesses good convergence characteristics. Numerica l examples are presented to compare the accuracy, efficiency and the r ate of convergence of the LSFEF. A p-version variational formulation i s presented for the axisymmetric heat conduction with temperature-depe ndent thermal conductivities. The numerical results obtained from the p-version LSFEF are compared with analytical solutions as well as thos e obtained from the p-version variational formulation. In some example s the LSFEF results are compared with refined h-models utilizing p-ver sion variational based elements. The pros and cons of both formulation s are demonstrated and discussed.