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Some Remarks on Functional Analysis (2014)
Book Chapter
Blowey, J. F., & Straughan, B. (2014). Some Remarks on Functional Analysis. In R. B. Hetnarski (Ed.), Encyclopedia of Thermal Stresses. Springer Verlag. https://doi.org/10.1007/978-94-007-2739-7_24

Functional analysis is a key tool in the study of partial differential equations which helps to answer key questions such as existence, well-posedness, and the class in which a solution should belong. We begin these remarks by introducing normed spac... Read More about Some Remarks on Functional Analysis.

Small- and waiting-time behavior of the thin-film equation (2007)
Journal Article
Blowey, J., King, J., & Langdon, S. (2007). Small- and waiting-time behavior of the thin-film equation. SIAM Journal on Applied Mathematics, 67(6), 1776-1807. https://doi.org/10.1137/060667682

We consider the small-time behavior of interfaces of zero contact angle solutions to the thin-film equation. For a certain class of initial data, through asymptotic analyses, we deduce a wide variety of behavior for the free boundary point. These are... Read More about Small- and waiting-time behavior of the thin-film equation.

A reaction-diffusion system of λ–ω type Part I: Mathematical analysis. (2005)
Journal Article
Blowey, J., & Garvie, M. (2005). Part I: Mathematical analysis. European Journal of Applied Mathematics, 16(1), 1-19. https://doi.org/10.1017/s0956792504005534

We study two coupled reaction-diffusion equations of the $\lambda$–$\omega$ type [11] in $d\,{\le}\,3$ space dimensions, on a convex bounded domain with a $C^2$ boundary. The equations are close to a supercritical Hopf bifurcation in the reaction kin... Read More about A reaction-diffusion system of λ–ω type Part I: Mathematical analysis..

Frontiers in Numerical Analysis: Durham 2002. (2003)
Book
Blowey, J., Craig, A., & Shardlow, T. (Eds.). (2003). Frontiers in Numerical Analysis: Durham 2002. Springer Verlag. https://doi.org/10.1007/978-3-642-55692-0

This book contains detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography... Read More about Frontiers in Numerical Analysis: Durham 2002..

Finite element approximation of an Allen-Cahn/Cahn-Hilliard system (2002)
Journal Article
Barrett, J., & Blowey, J. (2002). Finite element approximation of an Allen-Cahn/Cahn-Hilliard system. IMA Journal of Numerical Analysis, 22(1), 11-71. https://doi.org/10.1093/imanum/22.1.11

We consider an Allen–Cahn/Cahn–Hilliard system with a non-degenerate mobility and (i) a logarithmic free energy and (ii) a non-smooth free energy (the deep quench limit). This system arises in the modelling of phase separation and ordering in binary... Read More about Finite element approximation of an Allen-Cahn/Cahn-Hilliard system.

Finite element approximation of a model for order-disorder and phase separationin binary alloys (2001)
Presentation / Conference Contribution
Blowey, J., Barrett, J., Feistauer, M., Rannacher, R., & Kozel, K. (2001). Finite element approximation of a model for order-disorder and phase separationin binary alloys. In M. Feistauer, R. Rannacher, & K. Kozel (Eds.), Numerical Modelling in Continuum Mechanics: proceedings of the 4th summer conference held in Prague, 31 July - 4 August, 2000 (1-17)

Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System (2001)
Journal Article
Barrett, J. W., & Blowey, J. F. (2001). Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System. SIAM Journal on Numerical Analysis, 39(5), 1598-1624. https://doi.org/10.1137/s0036142900382144

We consider a fully practical finite element approximation of an Allen--Cahn/Cahn--Hilliard system with a degenerate mobility and a logarithmic free energy. This system arises in the modeling of phase separation and ordering in binary alloys. In addi... Read More about Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System.

On Fully Practical Finite Element Approximations of Degenerate Cahn-Hilliard Systems (2001)
Journal Article
Barrett, J., Blowey, J., & Garcke, H. (2001). On Fully Practical Finite Element Approximations of Degenerate Cahn-Hilliard Systems. ESAIM: Mathematical Modelling and Numerical Analysis, 35(4), 713-748. https://doi.org/10.1051/m2an%3A2001133

We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dime... Read More about On Fully Practical Finite Element Approximations of Degenerate Cahn-Hilliard Systems.

An Improved Error Bound for a Finite Element Approximation of a Model for Phase Separation of a Multi-Component Alloy with a Concentration Dependent Mobility Matrix (2001)
Journal Article
Barrett, J., & Blowey, J. (2001). An Improved Error Bound for a Finite Element Approximation of a Model for Phase Separation of a Multi-Component Alloy with a Concentration Dependent Mobility Matrix. Numerische Mathematik, 88(2), 255-297. https://doi.org/10.1007/pl00005445

Using a slightly different discretization scheme in time and adapting the approach in Nochetto et al. (1998) for analysing the time discretization error in the backward Euler method, we improve on the error bounds derived in (i) Barrett and Blowley (... Read More about An Improved Error Bound for a Finite Element Approximation of a Model for Phase Separation of a Multi-Component Alloy with a Concentration Dependent Mobility Matrix.

Finite element approximation of the Cahn-Hilliard equation with degenerate mobility. (1999)
Journal Article
Blowey, J., Barrett, J., & Garcke, H. (1999). Finite element approximation of the Cahn-Hilliard equation with degenerate mobility. SIAM Journal on Numerical Analysis, 37(1), 286-318. https://doi.org/10.1137/s0036142997331669

We consider a fully practical finite element approximation of the Cahn--Hilliard equation with degenerate mobility $$ \textstyle \frac{\partial u}{\partial t}= \del .(\,b(u)\, \del (-\gamma\lap u+\Psi'(u))) , $$ where $b(\cdot)\geq 0$ is a diffusiona... Read More about Finite element approximation of the Cahn-Hilliard equation with degenerate mobility..

Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility, (1999)
Journal Article
Blowey, J., & Barrett, J. (1999). Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility,. Mathematics of Computation, 68(226), 487-517. https://doi.org/10.1090/s0025-5718-99-01015-7

We consider the Cahn-Hilliard equation with a logarithmic free energy and non-degenerate concentration dependent mobility. In particular we prove that there exists a unique solution for sufficiently smooth initial data. Further, we prove an error bou... Read More about Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility,.

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy. (1999)
Journal Article
Blowey, J., & Barrett, J. (1999). An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy. ESAIM: Mathematical Modelling and Numerical Analysis, 33(5), 971-987. https://doi.org/10.1051/m2an%3A1999129

Using the approach in [5] for analysing time discretization error and assuming more regularity on the initial data, we improve on the error bound derived in [2] for a fully practical piecewise linear finite element approximation with a backward Euler... Read More about An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy..

Finite element approximation of a model for phase separation of a multi-component alloy with nonsmooth free energy and a concentration dependent mobility matrix. (1999)
Journal Article
Blowey, J., & Barrett, J. (1999). Finite element approximation of a model for phase separation of a multi-component alloy with nonsmooth free energy and a concentration dependent mobility matrix. Mathematical Models and Methods in Applied Sciences, 9(5), 627-663. https://doi.org/10.1142/s0218202599000336

We consider a model for phase separation of a multi-component alloy with nonsmooth free energy and a concentration dependent mobility matrix. In particular we prove that there exists a unique solution for sufficiently smooth initial data. Further, we... Read More about Finite element approximation of a model for phase separation of a multi-component alloy with nonsmooth free energy and a concentration dependent mobility matrix..

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy. (1999)
Journal Article
Blowey, J., & Barrett, J. (1999). An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy. IMA Journal of Numerical Analysis, 19(1), 147-168. https://doi.org/10.1093/imanum/19.1.147

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87) for analysing the time discretization error and assuming more regularity on the initial data, we improve on the error bound derived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,... Read More about An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy..

Finite element approximation of a fourth order nonlinear degenerate parabolic equation. (1998)
Journal Article
Blowey, J., Barrett, J., & Garcke, H. (1998). Finite element approximation of a fourth order nonlinear degenerate parabolic equation. Numerische Mathematik, 80(4), 525-556. https://doi.org/10.1007/s002110050377

We consider a fully practical finite element approximation of the fourth order nonlinear degenerate parabolic equation ut+∇.(b(u)∇δu)=0, where generically b(u):=|u|p for any given p∈(0,∞). An iterative scheme for solving the resulting nonlinear discr... Read More about Finite element approximation of a fourth order nonlinear degenerate parabolic equation..