Stability characteristics of time integration schemes for finite element solutions of conduction‐type problems

Abstract

Stability characteristics of two‐level, time‐integration algorithms are investigated, with particular reference to explicit schemes. Conditions for stability are expressed on the basis of algebraic estimates of the eigenvalues associated with the amplification matrices of the algorithm. The use of automatic symbolic manipulators allows an extension of these estimates to higher order and multidimensional elements. Eigenvectors are also evaluated algebraically and the resulting fundamental mode shapes are related to the onset of instabilities.

Citation

Comini, G. and Manzan, M. (1994), "Stability characteristics of time integration schemes for finite element solutions of conduction‐type problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 4 No. 2, pp. 131-142. https://doi.org/10.1108/EUM0000000004035