Special Bilinear Quadrilateral Elements For Locally Refined Finite Element Grids

A set of special bilinear quadrilateral elements are developed to handle irregular nodes on the interface between different refinement levels in 1-irregular meshes for the adaptive finite element method. With this alternative approach, irregular nodes are eliminated, and at the same time the C0 continuity at interelements is strictly ensured. The new elements simplify the refinement procedure and circumvent many inconveniences in local refinement with linear quadrilateral elements. Solutions to problems of a heat conduction, a reaction-diffusion, and incompressible and viscous flows past a circular cylinder are respectively presented to test the effectiveness of special elements. They demonstrate good accuracy and a potential applicability to more complex problems.

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