Time-harmonic elasticity with controllability and higher-order discretization methods

Higher Order Numerical Discretization Methods with Sobolev Norm Minimization

This paper presents a method of producing higher order discretization weights for linear differential and integral operators using the Minimum Sobolev Norm idea[1][2] in arbitrary geometry and grid configurations. The weight computation involves solving a severely ill-conditioned weighted least-squares system. A method of solving this system to very high-accuracy is also presented, based on the...

Higher-Order Discretization of Diffusion Terms in Residual-Distribution Methods

We discuss various higher-order discretization methods for diffusion terms in residual-distribution methods. Categorizing methods into two types: node-based (Galerkin methods) and cell-based (residual-distribution methods), we begin with the description of the basic low-order methods. We then consider two different approaches to extend these methods to higher-order: reconstruction and higher-or...

A-stable discontinuous Galerkin-Petrov time discretization of higher order

Higher order Galerkin time discretization for nonstationary incompressible flow

In this paper, we extend our work for the heat equation in [4] and for the Stokes equations in [5] to the nonstationary Navier-Stokes equations in two dimensions. We examine continuous Galerkin-Petrov (cGP) time discretization schemes for nonstationary incompressible flow. In particular, we implement and analyze numerically the higher order cGP(2)-method. For the space discretization, we use th...

Discretization methods with analytical solutions for a convection-reaction equation with higher-order discretizations

We introduce an improved second-order discretization method for the convection-reaction equation by combining analytical and numerical solutions. The method is derived from Godunov’s scheme, see [15] and [21], and uses analytical solutions to solve the one-dimensional convection-reaction equation. We can also generalize the second-order methods for discontinuous solutions, because of the analyt...