Outputs (74)

hp-adaptive two-grid discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows (2013)
Presentation / Conference Contribution
Congreve, S., Houston, P., & Wihler, T. P. hp-adaptive two-grid discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. Presented at Numerical Mathematics and Advanced Applications, ENUMATH 2011

We develop the a posteriori error analysis, with respect to a mesh-dependent energy norm, of two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian flows. The performance of the proposed estimators within an hp-adaptive... Read More about hp-adaptive two-grid discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows.

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows (2012)
Journal Article
Congreve, S., Houston, P., Süli, E., & Wihler, T. P. Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows. Manuscript submitted for publication

In this article we develop both the a priori and a posteriori error analysis of hp– version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ R^d, d = 2,... Read More about Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows.

Adaptivity and a Posteriori Error Control for Bifurcation Problems III: Incompressible Fluid Flow in Open Systems with O(2) Symmetry (2011)
Journal Article
Cliffe, A., Hall, E., Houston, P., Phipps, E., & Salinger, A. (2012). Adaptivity and a Posteriori Error Control for Bifurcation Problems III: Incompressible Fluid Flow in Open Systems with O(2) Symmetry. Journal of Scientific Computing, 52(1), 153-179. https://doi.org/10.1007/s10915-011-9545-8

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particula... Read More about Adaptivity and a Posteriori Error Control for Bifurcation Problems III: Incompressible Fluid Flow in Open Systems with O(2) Symmetry.

Discontinuous Galerkin methods for problems with Dirac delta source (2011)
Journal Article
Houston, P., & Wihler, T. P. Discontinuous Galerkin methods for problems with Dirac delta source. Manuscript submitted for publication

In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-un... Read More about Discontinuous Galerkin methods for problems with Dirac delta source.

Preconditioning high-order discontinuous Galerkin discretizations of elliptic problems (2011)
Presentation / Conference Contribution
Antonietti, P. F., & Houston, P. Preconditioning high-order discontinuous Galerkin discretizations of elliptic problems. Presented at 20th International Conference on Domain Decomposition Methods

Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs (2011)
Journal Article
Congreve, S., Houston, P., & Wihler, T. P. (2011). Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs. PAMM, 11(1), https://doi.org/10.1002/pamm.201110002

In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In thi... Read More about Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs.

Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows (2011)
Journal Article
Giani, S., & Houston, P. Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. Manuscript submitted for publication

In this article we consider the construction of general isotropic and anisotropic adaptive mesh refinement strategies, as well as hp-mesh refinement techniques, for the numerical approximation of the compressible Euler and Navier-Stokes equations. To... Read More about Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows.

Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem (2010)
Journal Article
Cliffe, A., Hall, E., Houston, P., Phipps, E. T., & Salinger, A. G. (2010). Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem. Communications in Computational Physics, 8(4), 845-865. https://doi.org/10.4208/cicp.290709.120210a

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, base... Read More about Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry (2010)
Journal Article
Cliffe, A., Hall, E., Houston, P., Phipps, E. T., & Salinger, A. G. Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry. 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 bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particula... Read More about Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry.

A new method for conditioning stochastic groundwater flow models in fractured media (2010)
Journal Article
Milne, A., Cliffe, A., Holton, D., Houston, P., Jackson, C. P., & Joyce, S. A new method for conditioning stochastic groundwater flow models in fractured media. Manuscript submitted for publication

Many geological formations consist of crystalline rocks that have very low matrix permeability but allow flow through an interconnected network of fractures. Understanding the flow of groundwater through such rocks is important in considering disposa... Read More about A new method for conditioning stochastic groundwater flow models in fractured media.