We give an overview of superconvergence phenomena in the finite element method for solving three-dimensional problems, in particular, for elliptic boundary value problems of second order over uniform meshes. Some difficulties with superconvergence on tetrahedral meshes are presented as well. For a given positive integer m we prove that there is no tetrahedralization of R3 whose all edges are m-...

• 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. • ...

We present a skeleton-based approach for mapping consistently a segmentation of a source mesh to a target mesh. The source and target meshes are semantically similar but their geometries may be different. We assume that the segmentation of the source mesh and the skeleton correspondence between the meshes are provided. Our method first establishes the skeleton-boundary correspondence and then p...

EEcient iterative methods for the numerical solution of three-dimensional acoustic scattering problems are considered. The underlying exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a non-reeecting boundary condition on the artiicial boundary. The nite element discretization of the approximate boundary value problem is performed using locally t...

A Dirichlet boundary value problem for a linear parabolic differential equation is studied on a rectangular domain in the x− t plane. The coefficient of the second order space derivative is a small singular perturbation parameter, which gives rise to parabolic boundary layers on the two lateral sides of the rectangle. It is proved that a numerical method, comprising a standard finite difference...

We propose a coarse-to-fine approach for generating fine and curved highorder tetrahedral meshes. The proposed approach is performed in three steps: (1) generate a coarse reference mesh; (2) map this to a coarse and curved highorder mesh; and (3) refine the curved high-order mesh. The approach provides high-order meshes that are valid, have the desired interpolation degree, and can be computed ...

Boundary-layer meshes are important for numerical simulations in computational fluid dynamics, including computational biofluid dynamics of air flow in lungs and blood flow in hearts. Generating boundary-layer meshes is challenging for complex biological geometries. In this paper, we propose a novel technique for generating prismatic boundary-layer meshes for such complex geometries. Our method...

This paper presents a mesh adaptation method for higher-order (p > 1) discontinuous Galerkin (DG) discretizations of the two-dimensional, compressible Navier–Stokes equations. A key feature of this method is a cut-cell meshing technique, in which the triangles are not required to conform to the boundary. This approach permits anisotropic adaptation without the difficulty of constructing meshes ...

The thesis presents a novel numerical method based on the high order Discontinuous Galerkin (DG) method for three dimensional electrostatic and electro-quasistatic field problems where materials are of very complex shape and may move over time. A well-known example is water droplets oscillating on the surface of high voltage power transmission line insulators. The electric field at the surface ...