All Outputs (75)

Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport (2024)
Journal Article

We introduce an hp–version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented in an almost... Read More about Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport.

Iterative solution methods for high-order/hp–DGFEM approximation of the linear Boltzmann transport equation (2024)
Journal Article

In this article we consider the iterative solution of the linear system of equations arising from the discretisation of the poly-energetic linear Boltzmann transport equation using a high-order/hp–version discontinuous Galerkin finite element approxi... Read More about Iterative solution methods for high-order/hp–DGFEM approximation of the linear Boltzmann transport equation.

Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems (2024)
Journal Article

In this article we consider the application of Euler’s homogeneous function theorem to- gether with Stokes’ theorem to exactly integrate families of polynomial spaces over general polygonal and polyhedral (polytopic) domains in two and three dimensio... Read More about Quadrature-Free Polytopic Discontinuous Galerkin Methods for Transport Problems.

Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes (2022)
Journal Article

This article considers the extension of two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic boundary value problems of monotone type to the case when agglomerated poly... Read More about Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes.

Linearization of the Travel Time Functional in Porous Media Flows (2022)
Journal Article

The travel time functional measures the time taken for a particle trajectory to travel from a given initial position to the boundary of the domain. Such evaluation is paramount in the postclosure safety assessment of deep geological storage facilitie... Read More about Linearization of the Travel Time Functional in Porous Media Flows.

Gibbs phenomena for Lq-best approximation in finite element spaces (2022)
Journal Article

Recent developments in the context of minimum residual finite element methods are paving the way for designing quasi-optimal discretization methods in non-standard function spaces, such as L q-type Sobolev spaces. For q → 1, these methods have demons... Read More about Gibbs phenomena for Lq-best approximation in finite element spaces.

High-Order Discontinuous Galerkin Methods on Polyhedral Grids for Geophysical Applications: Seismic Wave Propagation and Fractured Reservoir Simulations (2021)
Book Chapter

Eliminating Gibbs phenomena: A non-linear Petrov–Galerkin method for the convection–diffusion–reaction equation (2020)
Journal Article

In this article we consider the numerical approximation of the convection-diffusion-reaction equation. One of the main challenges of designing a numerical method for this problem is that boundary layers occurring in the convection-dominated case can... Read More about Eliminating Gibbs phenomena: A non-linear Petrov–Galerkin method for the convection–diffusion–reaction equation.

hp-Adaptive Iterative Linearization Discontinuous-Galerkin FEM for Quasilinear Elliptic Boundary Value Problems (2020)
Conference Proceeding

In this article we consider the a posteriori error analysis of hp-version discontinuous Galerkin finite element methods for the numerical solution of a second-order quasilinear elliptic boundary value problem of strongly monotone type. In particular,... Read More about hp-Adaptive Iterative Linearization Discontinuous-Galerkin FEM for Quasilinear Elliptic Boundary Value Problems.

An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids (2020)
Journal Article

In this article we design and analyze a class of two-level non-overlapping additive Schwarz preconditioners for the solution of the linear system of equations stemming from discontinuous Galerkin discretizations of second-order elliptic partial diffe... Read More about An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids.

Two?Grid hp ?DGFEMs on Agglomerated Coarse Meshes (2019)
Journal Article

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

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

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

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

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

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

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

hp-Adaptive discontinuous Galerkin methods for neutron transport criticality problems (2017)
Journal Article

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

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.