Fatih Celiker

Superconvergence of the numerical traces of discontinuous Galerkin and hybridized methods for convection-diffusion problems in one space dimension

In this paper, we uncover and study a new superconvergence property of a large class of finite element methods for one-dimensional convection-diffusion problems. This class includes discontinuous Galerkin methods defined in terms of numerical traces, discontinuous Petrov-Galerkin methods and hybridized mixed methods. We prove that the so-called numerical traces of both variables superconverge at all the nodes of the mesh, provided that the traces are conservative, that is, provided they are single-valued. In particular, for is local discontinuous Galerkin method, we show that the superconvergence is order 2p + 1 when polynomials of degree at most p are used. Extensive numerical results verifying our theoretical results are displayed.

Locking-Free Optimal Discontinuous Galerkin Methods for Timoshenko Beams

In this paper, we consider the so-called

Hybridizable Discontinuous Galerkin Methods for Timoshenko Beams

hp

Fast colour space transformations using minimax approximations

-version of discontinuous Galerkin methods for Timoshenko beams. We prove that, when the numerical traces are properly chosen, the methods display optimal convergence uniformly with respect to the thickness of the beam. These methods are thus free from shear locking. We also prove that, when polynomials of degree

On Euclidean norm approximations

p

Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Timoshenko Beams

are used, all the numerical traces superconverge with a rate of order

A projection-based error analysis of HDG methods for Timoshenko beams

h^{2p+1}/p^{2p+1}

On a class of nonlocal wave equations from applications

. Numerical experiments verifying the above-mentioned theoretical results are shown.

Nodal Superconvergence of SDFEM for Singularly Perturbed Problems

In this paper, we introduce a new class of discontinuous Galerkin methods for Timoshenko beams. The main feature of these methods is that they can be implemented in an efficient way through a hybridization procedure which reduces the globally coupled unknowns to approximations to the displacement and bending moment at the element boundaries. After displaying the methods, we obtain conditions under which they are well defined. We then compare these new methods with the already existing discontinuous Galerkin methods for Timoshenko beams. Finally, we display extensive numerical results to ascertain the influence of the stabilization parameters on the accuracy of the approximation. In particular, we find specific choices for which all the variables, namely, the displacement, the rotation, the bending moment and the shear force converge with the optimal order of k+1 when each of their approximations are taken to be piecewise polynomial of degree k≥0.

Comparison of Nonlocal Operators Utilizing Perturbation Analysis

Colour space transformations are frequently used in image processing, graphics and visualisation applications. In many cases, these transformations are complex non-linear functions, which prohibit their use in time-critical applications. A new approach called minimax approximations for colour space transformations (MACT) is presented. The authors demonstrate MACT on three commonly used colour space transformations. Extensive experiments on a large and diverse image set and comparisons with well-known multidimensional look-up table interpolation methods show that MACT achieves an excellent balance among four criteria: ease of implementation, memory usage, accuracy and computational speed.