16 citations · 25 across the 14 of their papers we have counts for
10 papers · 1 filter
Duality-Based Error Identities for Subgradient Flows Based on the Brézis-Ekeland-Nayroles Principle
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
We derive duality-based error identities for a broad class of subgradient flows induced by time-dependent convex integral functionals. Starting from the Bré…
Duality Framework for Flux Constrained Flow in Porous Media: Analysis and Numerics
Harbir Antil, Keegan L. A. Kirk, Felipe Pérez
We introduce and analyze Darcy flow through a saturated porous medium subject to bilateral constraints on the normal flux across a portion of the boundary. The problem is posed as…
A Finite Element Approximation of an Optimal Insulation Problem with Convective Heat Transfer
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
A finite element discretization of an optimal insulation problem with convective heat transfer is considered. The model is formulated as a non-smooth, two-variable convex minimizat…
A Hybridizable Discontinuous Galerkin Method for the Miscible Displacement Problem Under Minimal Regularity
Keegan L. A. Kirk, Beatrice Riviere
A numerical method based on the hybridizable discontinuous Galerkin method in space and backward Euler in time is formulated and analyzed for solving the miscible displacement prob…
Duality-Based Algorithm and Numerical Analysis for Optimal Insulation Problems on Non-Smooth Domains
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
This article develops a numerical approximation of a convex non-local and non-smooth minimization problem. The physical problem involves determining the optimal distribution, given…
A Discontinuous Galerkin Method for the Extracellular Membrane Intracellular Model
Rami Masri, Keegan L. A. Kirk, Eirill Hauge +1
We formulate and analyze interior penalty discontinuous Galerkin methods for coupled elliptic PDEs modeling excitable tissue, represented by intracellular and extracellular domains…
Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn-Hilliard problem
Keegan L. A. Kirk, Rami Masi, Beatrice Riviere
The mixed form of the Cahn-Hilliard equations is discretized by the hybridizable discontinuous Galerkin method. For any chemical energy density, existence and uniqueness of the num…
Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier--Stokes equations
Keegan L. A. Kirk, Ayçıl Çeşmelioǧlu, Sander Rhebergen
We prove that a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations converges to a weak solution as the time step and mesh size tend t…
Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier--Stokes equations
Keegan L. A. Kirk, Tamás L. Horváth, Sander Rhebergen
We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations. Key features of the numerical scheme include point-wis…
Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains
Keegan L. A. Kirk, Tamas L. Horvath, Aycil Cesmelioglu +1
This paper presents the first analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains. The analysis is b…