We present a comprehensive assessment of nodal and hybrid modal/nodal discontinuous Galerkin (DG) finite element solutions on a range of unstructured meshes to nonlinear shallow water flow with smooth solutions. The nodal DG methods on triangles and a tensor-product nodal basis on quadrilaterals are considered. The hybrid modal/nodal DG methods utilize two different synergistic polynomial bases...

In the present research, the elastic buckling of composite cross-ply elliptical cylindrical shells under axial compression is studied through finite element approach. The formulation is based on shear deformation theory and the serendipity quadrilateral eight-node element is used to study the elastic behavior of elliptical cylindrical shells. The strain-displacement relations are accurately acc...

Interpolation operators map a function u to an element Iu of a finite element space. Unlike more general approximation operators, interpolants are defined locally. Estimates of the interpolation error, i.e., the difference u− Iu, are of utmost importance in numerical analysis. These estimates depend on the size of the finite elements, the polynomial degree employed, and the regularity of u. In ...

Four quadrilateral elements for the Reissner-Mindlin plate model are considered. The elements are the stabilized MITC4 element of Lyly, Stenberg and Vihinen [27], the MIN4 element of Tessler and Hughes [35], the Q4BL element of Zienkiewicz et al [39] and the FMIN4 element of Kikuchi and Ishii [21]. For all elements except the Q4BL element, a unifying variational formulation is introduced, and o...

The work focuses on the development of a 2D quadrilateral element based Spectral Difference solver for viscous flow calculations, and the application of the p-multigrid method and implicit time-stepping to accelerate convergence. This paper extends the previous work by Liang et al (2009) on the p-multigrid method for 2D inviscid compressible flow, to viscous flows. The high-order spectral diffe...

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence....