6 papers
Duality Framework for Flux Constrained Flow in Porous Media: Analysis and Numerics
Harbir Antil, Keegan L. A. Kirk, Felipe Pérez
The paper develops a duality-based formulation for Darcy flow in saturated porous media with bilateral flux constraints on part of the boundary, analyzes its mathematical propertie…
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…
Convection Effects and Optimal Insulation: Modelling and Analysis
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
In this paper, we study an insulation problem that seeks to determine the optimal distribution of a given amount of insulating material coating an insulated boundary part $Î…
Modeling and Analysis of an Optimal Insulation Problem on Non-Smooth Domains
Harbir Antil, Alex Kaltenbach, Keegan L. A. Kirk
In this paper, we study an insulation problem that seeks the optimal distribution of a fixed amount of insulating material coating an insulated boundary $Î_I\subseteq \parti…
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…