Outputs (75)

Two‐Grid hp ‐DGFEMs on Agglomerated Coarse Meshes (2019)
Presentation / Conference Contribution
Congreve, S., & Houston, P. (2019, February). Two‐Grid hp ‐DGFEMs on Agglomerated Coarse Meshes. Presented at 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Vienna, Austria

We generalise the a priori error analysis of two‐grid hp‐version discontinuous Galerkin finite element methods for strongly monotone second‐order quasilinear elliptic partial differential equations to the case when coarse meshes consisting of general... Read More about Two‐Grid hp ‐DGFEMs on Agglomerated Coarse Meshes.

The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method (2019)
Journal Article
Houston, P., Muga, I., Roggendorf, S., & van der Zee, K. (2019). The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method. Computational Methods in Applied Mathematics, 19(3), 503-522. https://doi.org/10.1515/cmam-2018-0198

While it is classical to consider the solution of the convection-diffusion-reaction equation in the Hilbert space H10(Ω), the Banach Sobolev space W1,q0(Ω), 1 less than ∞ , is more general allowing more irregular solutions. In this paper we present a... Read More about The Convection-Diffusion-Reaction Equation in Non-Hilbert Sobolev Spaces: A Direct Proof of the Inf-Sup Condition and Stability of Galerkin’s Method.

Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods (2018)
Journal Article
Antonietti, P., Houston, P., & Pennesi, G. (2018). Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods. Journal of Scientific Computing, 77(3), 1339-1370. https://doi.org/10.1007/s10915-018-0802-y

In this paper we present efficient quadrature rules for the numerical approximation of integrals of polynomial functions over general polygonal/polyhedral elements that do not require an explicit construction of a sub-tessellation into triangular/tet... Read More about Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods.

Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem (2018)
Journal Article
Congreve, S., Houston, P., & Perugia, I. (2019). Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. Advances in Computational Mathematics, 45(1), 361-393. https://doi.org/10.1007/s10444-018-9621-9

In this article we develop an hp-adaptive refinement procedure for Trefftz discontinuous Galerkin methods applied to the homogeneous Helmholtz problem. Our approach combines not only mesh subdivision (h-refinement) and local basis enrichment (p-refin... Read More about Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem.

Automatic symbolic computation for discontinuous Galerkin finite element methods (2018)
Journal Article
Houston, P., & Sime, N. (2018). Automatic symbolic computation for discontinuous Galerkin finite element methods. SIAM Journal on Scientific Computing, 40(3), Article C327-C357. https://doi.org/10.1137/17M1129751

The implementation of discontinuous Galerkin finite element methods (DGFEMs) represents a very challenging computational task, particularly for systems of coupled nonlinear PDEs, including multiphysics problems, whose parameters may consist of power... Read More about Automatic symbolic computation for discontinuous Galerkin finite element methods.

Output feedback control of flow separation over an aerofoil using plasma actuators (2018)
Journal Article
Broglia, R., Choi, K.-S., Houston, P., Pasquale, L., & Zanchetta, P. (2018). Output feedback control of flow separation over an aerofoil using plasma actuators. International Journal of Numerical Analysis and Modeling, 15(6),

We address the problem of controlling the unsteady flow separation over an aerofoil, using plasma actuators. Despite the complexity of the dynamics of interest, we show how the problem of controlling flow separation can be formulated as a simple set... Read More about Output feedback control of flow separation over an aerofoil using plasma actuators.

An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems (2018)
Journal Article
Houston, P., & Wihler, T. P. (in press). An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems. Mathematics of Computation, https://doi.org/10.1090/mcom/3308

In this paper we develop an hp-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and an hp-versio... Read More about An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems.

hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes (2017)
Book
Cangiani, A., Dong, Z., Georgoulis, E. H., & Houston, P. (2017). hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes. (1). Springer Publishing Company. https://doi.org/10.1007/978-3-319-67673-9

hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems (2017)
Journal Article
Hall, E., Houston, P., & Murphy, S. (in press). hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems. SIAM Journal on Scientific Computing, 39(5), Article B916-B942

In this article we consider the application of high-order/hp-version adaptive discontinuous Galerkin finite element methods (DGFEMs) for the discretization of the keff-eigenvalue problem associated with the neutron transport equation. To this end, we... Read More about hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems.

An adaptive variable order quadrature strategy (2017)
Journal Article
Houston, P., & Wihler, T. P. (in press). An adaptive variable order quadrature strategy. Lecture Notes in Computational Science and Engineering, 119, https://doi.org/10.1007/978-3-319-65870-4_38

In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this way we aim t... Read More about An adaptive variable order quadrature strategy.