Mesh adaptation methods can improve the efficiency and accuracy of solutions to computational modeling problems. In many applications involving quadrilateral and hexahedral meshes, local modifications which maintain the original element type are desired. For triangle and tetrahedral meshes, effective refinement and coarsening methods that satisfy these criteria are available. Refinement methods...

A new four-node (non-flat) general quadrilateral shell element for geometric and material non-linear analysis is presented. The element is formulated using threedimensional continuum mechanics theory and it is applic­ able to the analysis of thin and thick shells. The for­ mulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.

A spectral element library has been developed and integrated with the M3D extended MHD code. The currently used linear triangular finite element implementation and the new high order quadrilateral spectral element implementation are directly compared on equilibrium, linear stability, and nonlinear evolution calculations run on the same problems. AMS subject classifications: 65M70 PACS: 52.65.Kj

In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in H-norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method. Mathematics Subject C...

Based on H-Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral meshes. The corresponding optimal order error estimate is derived by the interpolation technique instead of the generalized elliptic projection which is necessary for classical error estimates of fini...

In this paper we develop and analyze a family of mixed finite element methods for the numerical solution of the Stokes problem in two space dimensions. In these schemes, the pressure is interpolated on a mesh of quadrilateral elements, while the velocity is approximated on a triangular mesh obtained by dividing each quadrilateral into four triangles by its diagonals. Continuous interpolations o...

• Mixed methods for elastodynamics with weak symmetry. • Mixed finite elements for elasticity on quadrilateral meshes. • Finite element differential forms on curvilinear cubic meshes and their approximation properties. Numer. • Nonconforming tetrahedral mixed finite elements for elasticity. • Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Math. • ...