NEW PROGRESS IN SELF-ADAPTIVE ANALYSIS OF 2D PROBLEMS: FROM FEMOL TO FEM

Remarkable success has been made in the self-adaptive analysis of the 2D Finite Element Method of Lines (FEMOL). However, in order to further expand the application areas and improve the computing power and efficiency, it has been needed to extend the advanced self-adaptive technology of FEMOL to the realm of the most-commonly-used Finite Element Method (FEM). With recent intensive studying, the technology transfer from FEMOL to FEM in the self-adaptive analysis of 2D problems has initially and successfully been achieved. The present paper gives a brief overview and report about this advancement. Based on the concept of FEMOL and the Element Energy Projection (EEP) method for super-convergence computation, a “discretization and recovery by dimension” scheme was proposed. By using the proposed super-convergence computation scheme and an error-averaging method for mesh generation based on the solution on element edges, a series of difficulties in the “technology transfer” from FEMOL to FEM were overcome smartly, and as a result, a new type of adaptive analysis strategy for 2D FEM was proposed. Like the excellent performance in FEMOL, the algorithm could adaptively produce FEM results on arbitrary geometric domains with the displacement accuracy point-wisely satisfying the user specified error tolerance in max-norm. In addition, the algorithm overcomes the disadvantage of precision redundancy in the analytical direction of FEMOL, and significantly improves computational efficiency and enhances application flexibility. Numerous representative numerical examples were given to demonstrate the reliability and efficiency of the proposed algorithm.