On the constants in hp-finite element trace inverse inequalities

  title={On the constants in hp-finite element trace inverse inequalities},
  author={Tim Warburton and Jan S. Hesthaven},
  journal={Computer Methods in Applied Mechanics and Engineering},
In this paper, we estimate the constants in the inverse inequalities for the nite element functions. Furthermore, we obtain the least upper bounds of the constants in inverse inequalities for the
On the Constants in Inverse Inequalities in L 2
In this paper we determine the constants in multivariate Markov inequalities in the L2-norm on an interval, a triangle and a tetrahedron. Using orthonormal polynomials, we derive explicit expression
Explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements
This paper derives new trace inequalities for NURBS-mapped domains with Sobolev-type inequalities, and compares the bounding constants appearing in the explicit trace inequalities with numerically computed optimalbounding constants.
Symmetric Interior Penalty Galerkin Method for Elliptic Problems
Computable lower bounds of the penalty parameters for stable and convergent symmetric interior penalty Galerkin methods are presented and the explicit dependence of the coercivity constants with respect to the polynomial degree and the angles of the mesh elements is derived.
Technical Note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes
We obtain a computable lower bound on the value of the interior penalty parameters sufficient for the existence of a unique discontinuous Galerkin finite element approximation of a second order
Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex
Convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2.5 is studied.
Continuous Interior Penalty hp-Finite Element Methods for Transport Operators
A continuous interior penalty hp-finite element method that penalizes the jump of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for first-order and


On the Constants in Some Inverse Inequalities for Finite Element Functions
We determine the constants in some inverse inequalities for finite element functions. These constants are crucial for the correct calibration of a posteriori error estimators. Résumé: Pour
Spectral approximations on the triangle
  • R. G. Owens
  • Mathematics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1998
In this paper we describe a new family of polynomials which are eigenfunctions of a singular Sturm–Liouville problem on the triangle T 2 ={(x,y):x≥0,y≥0,x+y1}. The polynomials are shown to be
P- and hp- finite element methods : theory and applications in solid and fluid mechanics
Variational formulation of boundary value problems The Finite Element Method (FEM): definition, basic properties hp- Finite Elements in one dimension hp- Finite Elements in two dimensions Finite
Spectral methods on triangles and other domains
This article shows how to obtain multidimensional spectral methods as a warped product of one-dimensional spectral methods, thus generalizing direct (tensor) products. This generalization includes
Hp-dgfem for Partial Diierential Equations with Nonnegative Characteristic Form
We develop the error analysis for the hp-version of a discontinuous nite element approximation to second-order partial diierential equations with non-negative characteristic form. This class of
The finite element method for elliptic problems
  • P. Ciarlet
  • Mathematics
    Classics in applied mathematics
  • 2002
From the Publisher: This book is particularly useful to graduate students, researchers, and engineers using finite element methods. The reader should have knowledge of analysis and functional
Orthogonal Polynomials
In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
Discontinuous Galerkin methods
The exposition of the ideas behind the devising of these methods as well as on the mechanisms that allow them to perform so well in such a variety of problems are concentrated on.
Two-Variable Analogues of the Classical Orthogonal Polynomials