Higher order methods for transient diffusion analysis

Abstract In this paper the finite element approach is examined for transient heat conduction and moisture migration problems. In particular, several finite element in time algorithms are developed based on Hermitian expansions of increasing order which are then compared with Pade approximations and alternative Norsett formulas. The individual time operators are investigated with regard to 1. a)accuracy of the incremental algorithm, 2. b)stability and implications of the integration of stiff systems, 3. c)computational implementation of higher order operators. After a thorough assessment of each family an incremental step-by-step algorithm is presented in which the solution of the linear expansion is corrected for higher order accuracy. To this end an iterative improvement technique is developed which does not destroy the sparse structure of the initial system matrices or increase their order. The theoretical exposition is concluded with numerical examples to compare the solution effort and the accuracy of the different operators.

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