All Outputs (75)

Discontinuous Galerkin Methods for the Biharmonic Problem
Journal Article

This work is concerned with the design and analysis of hp-version discontinuous Galerkin (DG) finite element methods for boundary-value problems involving the biharmonic operator. The first part extends the unified approach of Arnold, Brezzi, Cockbur... Read More about Discontinuous Galerkin Methods for the Biharmonic Problem.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity
Journal Article

We consider the a posteriori error analysis and hp-adaptation strategies for hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined co... Read More about Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity.

Error estimation and adaptive mesh refinement for aerodynamic flows
Book Chapter

This lecture course covers the theory of so-called duality-based a posteriori error estimation of DG finite element methods. In particular, we formulate consistent and adjoint consistent DG methods for the numerical approximation of both the compress... Read More about Error estimation and adaptive mesh refinement for aerodynamic flows.

A Pre-processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems
Journal Article

We propose a pre-processing mesh re-distribution algorithm based upon harmonic maps employed in conjunction with discontinuous Galerkin approximations of advection-diffusion-reaction problems. Extensive two-dimensional numerical experiments with dif... Read More about A Pre-processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems.

A posteriori error estimation for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations
Journal Article

We develop the a posteriori error estimation of interior penalty discontinuous Galerkin discretizations for H(curl)-elliptic problems that arise in eddy current models. Computable upper and lower bounds on the error measured in terms of a natural (me... Read More about A posteriori error estimation for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations.

Discontinuous Galerkin Computation of the Maxwell Eigenvalues on Simplicial Meshes
Journal Article

This paper is concerned with the discontinuous Galerkin approximation of the Maxwell eigenproblem. After reviewing the theory developed in [5], we present a set of numerical experiments which both validate the theory, and provide further insight reg... Read More about Discontinuous Galerkin Computation of the Maxwell Eigenvalues on Simplicial Meshes.

Enhancing SPH using moving least-squares and radial basis functions
Journal Article

In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using... Read More about Enhancing SPH using moving least-squares and radial basis functions.

Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation
Journal Article

In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier--Stokes equations. In particular... Read More about Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation.

Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation
Journal Article

In this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier-Stokes equations. For the discretization of the leading order terms, we propose employing the gene... Read More about Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation.

A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems
Journal Article

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error ar... Read More about A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis
Journal Article

We consider the a priori error analysis of hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local finite... Read More about Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis.

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes
Journal Article

In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational me... Read More about Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes.

A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics
Journal Article

We introduce and analyze a discontinuous Galerkin method for the numerical discretization of a stationary incompressible magnetohydrodynamics model problem. The fluid unknowns are discretized with inf-sup stable discontinuous P^3_{k}-P_{k-1} elements... Read More about A Mixed Discontinuous Galerkin Method for Incompressible Magnetohydrodynamics.

An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems
Journal Article

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approxi... Read More about An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems.

Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows
Journal Article

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible Navier-Stokes equations. Parti... Read More about Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows.