Elements Of Different Orders Research Articles

ACCURACY COMPARISON OF CONTROL-VOLUME AND BUBNOV-GALERKIN FINITE-ELEMENT METHODS FOR HEAT CONDUCTION PROBLEMS

The two-dimensional heat conduction equation is solved by control-volume and Bubnov-Galerkin finite-element methods. The accuracy reached is estimated on the basis of five test problems for which exact analytical solutions are available. The comparison concerns the calculation of temperature distribution and the computation of nodal heat flow rates over external and internal boundaries. In the numerical solution, rectangular elements of different orders are used and the element integrals are evaluated in closed form, thus avoiding all the errors not connected directly with the discretization process.

Deriving shape functions for triangular mid-edge finite elements through blending-function interpolation

In a finite-element mesh, mid-edge elements are often used to transition between elements of different orders. A mid-edge element has no interior nodes, and typically has different numbers of nodes along its edges. Lacombe and Bédard have devised a systematic method for obtaining the shape functions of arbitrary mid-edge triangular elements, based on a particular interpolation scheme in the triangle. Unfortunately the resulting shape functions involve complicated rational terms. This paper presents three interpolation schemes that lead to polynomial shape functions for the mid-edge triangular elements.

A two-dimensional mesh generator for variable order triangular and rectangular elements

An improved method is presented for generating variable order elements by superelement generation. This method is simple to apply and requires less execution time in comparison with other variable order mesh generators. Depending on geometrical complexity and material variation, the superelements are manually determined to be refined into high or low order elements. Different mesh generation subroutines are employed to generate elements of different orders. The refined elements of different orders are finally patched to form a hybrid mesh. A FORTRAN program is given to generate finite element meshes of linear and quadratic triangular and rectangular elements automatically.

The boundary element method in elasticity

This paper describes the application of the boundary element method in elasticity starting by discussing the basic weighted residual expressions. Boundary elements of different orders are presented and discussed, together with the numerical integration schemes. The relationships are presented for three dimensional elasticity and specialized to the two dimensional case. Results are presented and discussed, specially in relation to finite elements and other “domain” type techniques.

Simplex elements of C0 continuity with varying polynomial degrees

AbstractA hierarchical approach is used to construct the simplex elements which permits easy merging of elements of different orders. The explicit interpolation functions and the algorithm of using such elements are presented.