UC Davis

This dissertation introduces a novel finite element method called the extended-stencilfinite element method (ESFEM). The ESFEM uses conventional finite element meshes to produce moderately high order polynomial element interpolants. The “nodal stencil” of the ESFEM is extended such that elements reference nodal values of other elements. This extension increases the nodal data available to an element. On each face of the element, a polynomial fit is performed to the nodal data. These “face polynomials” are then used as constraints in the polynomial fit of the element interpolant to the nodal data. Because the element interpolants are formulated independently from other element interpolants, the ESFEM is generally nonconforming. However, convergence is achieved by constraining the interpolant to ensure passage of the so called F-E-M-Test. The ESFEM was implemented into a finite element code base, and the results of the numerical examples show improved accuracy over the conventional finite element method in problems exhibiting shear locking, volumetric locking, and mesh distortion. In particular, the ESFEM enables an efficient use of a mesh’s degrees of freedom by using a polynomial fit to form the element interpolants.