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Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows (2013)
Conference Proceeding
Cliffe, A., Hall, E., & Houston, P. (2013). Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows.

In this article we consider the a posteriori error estimation and adaptive mesh refinement of hp-version discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations... Read More about Application of hp-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows.

Mirror symmetry and Fano manifolds (2013)
Conference Proceeding
Coates, T., Corti, A., Galkin, S., Golyshev, V., & Kasprzyk, A. M. (2013). Mirror symmetry and Fano manifolds.

We consider mirror symmetry for Fano manifolds, and describe how one can recover the classification of 3-dimensional Fano manifolds from the study of their mirrors. We sketch a program to classify 4-dimensional Fano manifolds using these ideas.

Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration (2013)
Conference Proceeding
Congreve, S., & Houston, P. (2013). Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration.

In this paper 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 based on the application of a single step of a no... Read More about Two-grid hp-DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration.

hp-adaptive two-grid discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows (2013)
Conference Proceeding
Congreve, S., Houston, P., & Wihler, T. P. (2013). hp-adaptive two-grid discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows.

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.