Mixed finite element formulation for the solution of parabolic problems Original Research Article

A mixed formulation of the finite element method is used to establish a higher-order incremental method for the solution of parabolic equations. The displacement and velocity fields (in the terminology of Solid Mechanics) are approximated independently in time using a hierarchical, adaptive basis. Three time bases are tested, namely polynomial, radial and wavelet bases. The time approximation criterion ensures stability and preserves parabolicity. The resulting discretization in the time domain leads to an uncoupled governing system in the space dimension. This system can be subsequently solved using the alternative formulations for the finite element and boundary element methods. The application of the conventional (conform displacement) formulation of the finite element method is illustrated. Particular attention is given to the extension of Pian- and Trefftz-type hybrid stress finite elements for transient analysis in the time domain. The performance of the coupled time-space integration method is assessed and the results obtained are compared with the results reported in the literature for alternative time integration procedures.