Nonhomogeneous boundary conditions and curved triangular finite elements

On Symmetric Hyperbolic Boundary Problems with Nonhomogeneous Conservative Boundary Conditions

Symmetric hyperbolic systems with nonhomogeneous conservative boundary conditions are considered. Existence, uniqueness, and regularity are established for the boundary value problem and the initial-boundary value problem. This boundary problem is not strongly well-posed in L2, a loss of derivatives is observed. Minimal regularity assumptions on the coefficients of the operator are made.

Comparison of some isoparametric mappings for curved triangular spectral elements

Implementation of nonhomogeneous dirichlet boundary conditions in the p version of the finite element method

Various methods for treating nonhomogeneous Dirichlet boundary conditions for the p-version of the finite element method are presented. These methods are theoretically and comrutationally analyzed. Numerical experimentations are given. They clearly illustrate the importance of the right treatment of the nonhomogeneous Dirichlet boundary conditions.

Triangular Elements in the Finite Element Method

For a plane polygonal domain Q and a corresponding (general) triangulation we define classes of functions pmix, v) which are polynomials on each triangle and which are in C^'CQ) and also belong to the Sobolev space ^""^'(n). Approximation theoretic properties are proved concerning these functions. These results are then applied to the approximate solution of arbitrary-order elliptic boundary va...

Derivative Superconvergence of Equilateral Triangular Finite Elements

Derivative superconvergent points under locally equilateral triangular mesh for both the Poisson and Laplace equations are reported. Our results are conclusive. For the Poisson equation, symmetry points are only superconvergent points for cubic and higher order elements. However, for the Laplace equation, most of superconvergent points are not symmetry points, which are reported for the first t...