Aspects of goal-oriented model-error estimation in convection-diffusion problems

For goal-oriented model adaptation a model-error estimator is required to drive the adaptation process. In recent years publications have appeared on the dual-weighted residual (DWR) method in the application of model-error estimation in output functionals. In this paper we study the application of the DWR method for convection-diffusion...

Error convergence of the Least-Squares Spectral Element formulation of the linear advection-reaction equation

This paper discusses the use of the Least-Squares Spectral Element Method in solving the linear, 1-dimensional advection-reaction equation. Well-posedness of the Least-Squares formulation will be derived. The formulation and its results will be compared to the standard Galerkin Spectral Element Method.

Application of Least-Squares Spectral Element Methods to Polynomial Chaos

This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.

Error convergence of the Least-Squares Spectral Element formulation of the linear advection-reaction equation

This paper discusses the use of the Least-Squares Spectral Element Method in solving the linear, 1-dimensional advection-reaction equation. Well-posedness of the Least-Squares formulation will be derived. The formulation and its results will be compared to the standard Galerkin Spectral Element Method.

Least-squares spectral element method with implicit time integration for the inviscid Burgers equation

This paper describes the use of the Least-Squares Spectral Element Method for non-linear hyperbolic equations. The one-dimensional inviscid Burgers equation is specifically subject of investigation. A second order backward difference method is used for time stepping. The behaviour of this formulation is examined by application to a testcase...

Aspects of goal-oriented model-error estimation in convection-diffusion problems

For goal-oriented model adaptation a model-error estimator is required to drive the adaptation process. In recent years publications have appeared on the dual-weighted residual (DWR) method in the application of model-error estimation in output functionals. In this paper we study the application of the DWR method for convection-diffusion...

Time Dependent Flow Simulations using the Least Squares Spectral Element Method with Direct Minimization

In this work a new approach to time dependent problems in combination with the Least-Squares Spectral Element Method (LSQSEM) will be discussed. Various time-stepping formulations will be presented. These time-stepping formulations will be compared to the full space-time formulation. It will be shown that time-stepping formulations give accurate...

Time Dependent Flow Simulations using the Least Squares Spectral Element Method with Direct Minimization

In this work a new approach to time dependent problems in combination with the Least-Squares Spectral Element Method (LSQSEM) will be discussed. Various timestepping formulations will be presented. These time-stepping formulations will be compared to the full space-time formulation. It will be shown that time-stepping formulations give accurate...