Curved triangular finite $C^m$-elements

Comparison of some isoparametric mappings for curved triangular spectral elements

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...

Mixed Finite Elements as Finite Differences for Elliptic Equations on Triangular Elements

Preconditioned Chebyshev collocation methods and triangular finite elements

This paper analyzes triangular finite elements for the preconditioning of Chebyshev collocation solutions of elliptic boundary value problems. Results are given for scalar model problems and for both Stokes and Navier-Stokes equations.