Effect of Elemental Shape and Modeling of Mixed Hybrid FEM on Numerical Solution

AbstractMixed Hybrid Finite element method, MHF, is known to be an efficient and powerful analyzing technique with satisfactory accuracy when differentiated variables should be evaluated, such as flow velocity based on velocity potential theory or stress calculated from displacement. On the other hand, it is known that the calculation accuracy and efficiency are affected by elemental shape and modeling. The aim of this study is to confirm the efficiency and accuracy of MHF by comparing it with FEM, and to discuss optimum elemental shapes and modeling. MHF, unlike FEM, evaluates the velocity potential and the flux on the element boundaries not at the element nodes; consequently, the material or mass balance of each element due to flow-in and flow-out through the boundaries can be strictly estimated. The flow velocity within an element, however, should be interpolated by those values on the boundaries, and a distinctive shape function, known as the Raviart-Thomas shape function, becomes necessary. The authors established the MHF formulation for arbitrary shaped elements with 3 and 4 boundaries, and numerically investigated its efficiency and accuracy with various shapes of elements. Through this study, it was confirmed that MHF can evaluate accurate flow velocity with a fewer number of elements than those of FEM. In addition, the effect of shape and modeling of elements on the numerical results were discussed to obtain better accuracy even if the total number of the elements is kept constant