All Outputs (5)

Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows (2014)
Journal Article
Giani, S., & Houston, P. (2014). Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows. Journal of Computational and Applied Mathematics, 270, 32-42. https://doi.org/10.1016/j.cam.2014.03.007

In this article we consider the application of goal-oriented mesh adaptation to problems posed on complicated domains which may contain a huge number of local geometrical features, or micro-structures. Here, we exploit the composite variant of the di... Read More about Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows.

A hp-adaptive discontinuous Galerkin method for plasmonic waveguides (2014)
Journal Article
Giani, S. (2014). A hp-adaptive discontinuous Galerkin method for plasmonic waveguides. Journal of Computational and Applied Mathematics, 270, 12-20. https://doi.org/10.1016/j.cam.2014.03.009

In this paper we propose and analyse a hphp-adaptive discontinuous finite element method for computing electromagnetic modes of propagation supported by waveguide structures comprised of a thin lossy metal film of finite width embedded in an infinite... Read More about A hp-adaptive discontinuous Galerkin method for plasmonic waveguides.

Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains (2014)
Journal Article
Antonietti, P., Giani, S., & Houston, P. (2014). Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains. Journal of Scientific Computing, 60(1), 203-227. https://doi.org/10.1007/s10915-013-9792-y

In this article we consider the application of Schwarz-type domain decomposition preconditioners for discontinuous Galerkin finite element approximations of elliptic partial differential equations posed on complicated domains, which are characterized... Read More about Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains.

hp–Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains (2014)
Journal Article
Giani, S., & Houston, P. (2014). hp–Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Numerical Methods for Partial Differential Equations, 30(4), 1342-1367. https://doi.org/10.1002/num.21872

In this article, we develop the a posteriori error estimation of hp–version discontinuous Galerkin composite finite element methods for the discretization of second-order elliptic partial differential equations. This class of methods allows for the a... Read More about hp–Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains.

An a-posteriori error estimate for hp-adaptive DG methods for convection–diffusion problems on anisotropically refined meshes (2014)
Journal Article
Giani, S., Schötzau, D., & Zhu, L. (2014). An a-posteriori error estimate for hp-adaptive DG methods for convection–diffusion problems on anisotropically refined meshes. Computers and Mathematics with Applications, 67(4), 869-887. https://doi.org/10.1016/j.camwa.2012.10.015

We prove an a-posteriori error estimate for hphp-adaptive discontinuous Galerkin methods for the numerical solution of convection–diffusion equations on anisotropically refined rectangular elements. The estimate yields global upper and lower bounds o... Read More about An a-posteriori error estimate for hp-adaptive DG methods for convection–diffusion problems on anisotropically refined meshes.