HIGHER-ORDER SPECTRAL/HP FEM APPROXIMATION
This study deals with the use of high-order spectral/hp approximation functions in finite element models of various of non-linear boundary-value and initial-value problems arising in the fields of structural mechanics and viscous fluid flows. For many of these classes of problems, the high-order (typically p = 4) spectral/hp finite element technology offers many theoretical as well as computational advantages over traditional low-order (typically p = 2) finite elements. For instance, higher-order spectral/hp finite element procedures allow us to develop robust structural elements for beams, plates, and shells in a purely displacement-based setting, which avoid all forms of numerical locking. The higher-order spectral/hp basis functions avoid the interpolation error in the numerical schemes, there by, making them accurate and stable. Furthermore, for fluid flows, when combined with least-squares variational principles, such technology allows us to develop efficient finite element models that always yield a symmetric positive-definite (SPD) coefficient matrix, and thereby robust direct or iterative solvers can be used. Also, the use of spectral/hp finite element technology results in a better conservation of physical quantities (like dilatation, volume, mass) and stable evolution of variables with time for transient flows.
Higher-order traditional weak-form Galerkin finite element models for shear-deformable elastic shell structures
Higher-order least-squares formulations for the Navier-Stokes equations governing flows of viscous incompressible fluids.