Outputs (74)

Enhancing SPH using moving least-squares and radial basis functions
Journal Article
Brownlee, R., Houston, P., Levesley, J., & Rosswog, S. Enhancing SPH using moving least-squares and radial basis functions

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.

Error estimation and adaptive mesh refinement for aerodynamic flows
Book Chapter
Hartmann, R., & Houston, P. Error estimation and adaptive mesh refinement for aerodynamic flows. In H. Deconinck (Ed.), Proceedings of the 36THCFD/Adigma course on HP-adaptive and HP-multigrid methods. von Karman Institute for Fluid Dynamics

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.

Discontinuous Galerkin Computation of the Maxwell Eigenvalues on Simplicial Meshes
Journal Article
Buffa, A., Houston, P., & Perugia, I. Discontinuous Galerkin Computation of the Maxwell Eigenvalues on Simplicial Meshes

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.

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

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.

A Pre-processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems
Journal Article
Antonietti, P. F., & Houston, P. A Pre-processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems. Manuscript submitted for publication

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.

Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows
Journal Article
Cliffe, A., Hall, E., & Houston, P. Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows. Manuscript submitted for publication

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.

Two-grid hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs
Journal Article
Congreve, S., Houston, P., & Wihler, T. P. Two-grid hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs. Manuscript submitted for publication

In this article we propose a class of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of a second-order quasilinear elliptic boundary value problem of monotone type. The key idea in this setting... Read More about Two-grid hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity
Journal Article
Georgoulis, E. H., Hall, E., & Houston, P. Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity. Manuscript submitted for publication

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.

An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems
Journal Article
Georgoulis, E. H., Houston, P., & Virtanen, J. An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems. Manuscript submitted for publication

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.

Discontinuous Galerkin Methods for the Biharmonic Problem
Journal Article
Georgoulis, E. H., & Houston, P. Discontinuous Galerkin Methods for the Biharmonic Problem. Manuscript submitted for publication

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.