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On the optimization of the fixed‐stress splitting for Biot's equations
(Peer reviewed; Journal article, 2019)In this work, we are interested in efficiently solving the quasi‐static, linear Biot model for poroelasticity. We consider the fixed‐stress splitting scheme, which is a popular method for iteratively solving Biot's equations. ... -
On the postage stamp problem with three stamp denominations, III
(Department of Pure Mathematics report no. 30, Research report, 1984-01) -
On the rate of convergence of alternating minimization for non-smooth non-strongly convex optimization in Banach spaces
(Journal article; Peer reviewed, 2022)In this paper, the convergence of the fundamental alternating minimization is established for non-smooth non-strongly convex optimization problems in Banach spaces, and novel rates of convergence are provided. As objective ... -
On the Relation between Surface Profiles and Internal Flow Properties in Long-Wave Models
(Doctoral thesis, 2017-03-10)In this work, we investigate the internal velocity field in a number of Boussinesq models in non-uniform situations. A coupled BBM-BBM type system of equations is derived in the assumption of water wave propagating over ... -
On the relationship between multiple porosity models and continuous time random walk
(Conference lecture, 2010)We derive a multiple porosity model based on the continuous time random walk model (CTRW). In particular, we show how the parameters of the multiple porosity models relate to the transition probability function which is ... -
On the shoaling of solitary waves in the KdV equation
(Journal article; Peer reviewed, 2014)The waveheight change in surface waves with a sufficiently slow variation in depth is examined. Using a new formulation of the energy flux associated to waves modeled by the Korteweg-de Vries equation, a system of three ... -
On the Solution of the Solitary Wave Problem
(Department of Applied Mathematics report, Research report, 1997-07) -
On the Stability of a Magnetized Plasma with a Continuous Density Gradient in a Uniform External Force Field
(Department of Applied Mathematics report, Research report, 1964-06) -
On the stability of plane inviscid Couette flow
(Department of Applied Mathematics report, Research report, 1966-11) -
On the unique continuation of solutions to non-local non-linear dispersive equations
(Journal article; Peer reviewed, 2020)We prove unique continuation properties of solutions to a large class of nonlinear, non-local dispersive equations. The goal is to show that if u1,u2 are two suitable solutions of the equation defined in Rn×[0,T] such that ... -
On the uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations.
(Department of Applied Mathematics report, Research report, 2002-04) -
On the Uniqueness and Stability of Entropy Solutions of nonlinear degenerate parabolic Equations with rough Coefficients
(Department of Applied Mathematics report, Research report, 2000-05) -
On the use of the Richtmyer procedure to compute a finite amplitude sound beam from a piston source
(Department of Applied Mathematics report, Research report, 1987-04-03) -
On the use of vertically averaged models to simulate CO2 migration in a layered saline aquifer
(Master thesis, 2010-06-01)Geologic and flow characteristics such as permeability and porosity, capillary pressure, geologic structure, and thickness all influence and affect CO2 plume distribution to varying degrees. These parameters do not necessarily ... -
On weak solutions and a covergent numerical scheme for the compressible Navier-Strokes Equations
(Journal article, 2015-02-26)In this paper, the three-dimensional compressible Navier-Stokes equations are considered on a periodic domain. We propose a semi-discrete numerical scheme and derive a priori bounds that ensures that the resulting system ... -
Open-source MATLAB implementation of consistent discretisations on complex grids
(Peer reviewed; Journal article, 2011-08-02)Accurate geological modelling of features such as faults, fractures or erosion requires grids that are flexible with respect to geometry. Such grids generally contain polyhedral cells and complex grid-cell connectivities. ... -
An Open-Source Toolchain for Simulation and Optimization of Aquifer-Wide CO2 Storage
(Peer reviewed; Journal article, 2016-02-04)Planning and execution of large-scale, aquifer-wide CO2 storage operations will require extensive use of computer modelling and simulations. The required computational tools will vary depending on the physical characteristics ... -
An Operator Splitting Method for Convection-Diffusion Equations
(Department of Applied Mathematics report, Research report, 1996-01) -
Operator Splitting Methods for Degenerate Convection-Diffusion Equations I: Convergence and Entropy Estimates
(Department of Applied Mathematics report, Research report, 1999-10) -
Operator splitting Methods for degenerate Convection-diffusion Equations II: Numerical Examples with Emphasis on Reservoir Simulation and Sedimentation
(Department of Applied Mathematics report, Research report, 1999-12)