NEW PROGRESS IN ADAPTIVE TIME-STEPPING FOR TIME INTEGRATION ANALYSIS: FROM CONDENSED ELEMENT TO REDUCED ELEMENT

It has been found in research that the successful implementation of adaptive time-stepping, measured by maximum norm, for time integration analysis by the finite element method requires the accuracy ratio between the nodal solution and element solution to be no less than 2. In other words, if the element accuracy is O(h^\overline m + 1) with \overline m -degreed element, the nodal accuracy should be best up to O(h^2\overline m + 2) . The condensed element proposed by the authors meets this requirement and has great performance in time-stepping adaptivity. Further, it has been found that the solution of the conventional element of degree \overline m + 1 contains the complete solution of the condensed element of degree \overline m . Thus, a simple and efficient element algorithm, called the reduced element, is proposed in this paper, which needs neither additional condensing procedure and nodal accuracy improvement, nor super-convergence calculation needed in other element models. The paper gives a brief description of the new progress in this related study with some preliminary numerical examples given to show the feasibility and effectiveness of the proposed approach.