EXPLORATION ON SUPER-CONVERGENT SOLUTIONS OF 3D FEM BASED ON EEP METHOD

In the super-convergence computation of a 2D Finite Element Method (FEM), the "discretization and recovery by dimension" scheme has basically formed by taking the Finite Element Method of Lines (FEMOL) as a bridge and iteratively by adopting the super-convergent formulas derived from the Element Energy Projection (EEP) method. However, when applying this idea to 3D problems, it occurs a puzzle that the EEP solutions (including displacements and derivatives) of 1D problems all share the same super-convergence order whereas those of 2D problems can hardly do. Recent studies show that in order to obtain the EEP super-convergent solution of a 3D problem, the displacement of a 2D problem with the least super-convergence order is merely necessary. Following this idea, this paper derives EEP super-convergent formulas for 3D hexahedron elements on irregular meshes, proposes an implementation scheme, and verifies its effectiveness with numerical examples.