Efficient linear and nonlinear heat conduction with a quadrilateral element
Abstract
A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using onepoint quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2, and 1 for the normalized stabilization parameter lead to the 5point, 9point finite difference, and fully integrated finite element operators, respectively, for rectangular meshes and have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 March 1983
 Bibcode:
 1983STIN...8320033L
 Keywords:

 Conductive Heat Transfer;
 Finite Element Method;
 Linear Systems;
 Nonlinear Systems;
 Quadratures;
 Eigenvalues;
 Finite Difference Theory;
 Numerical Stability;
 Problem Solving;
 Stiffness Matrix;
 Fluid Mechanics and Heat Transfer