M. J. Baines

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Deformable models of elastic structures have been proposed for use in image analysis. Previous work has used a variational approach, based on the Euler-Lagrange theory. In this paper an alternative mathematical treatment is introduced, based on a direct minimisation of the underlying energy integral using the Finite Element Method. The method is outlined(More)
A new family of mathematical functions to fit longitudinal growth data is described. All members derive from the differential equation dh/dt = s(t). (h1-h) where h1 is adult size and s(t) is a function of time. The form of s(t) is given by one of many functions, all solutions of differential equations, thus generating a family of different models. Three(More)
This paper discusses the problem of constructing a locally optimal mesh for the best L 2 approximation of a given function by discontinuous piecewise polynomials. In the one-dimensional case, it is shown that, under certain assumptions on the approximated function, Baines' algorithm [M. for piecewise linear or piece-wise constant polynomials produces a mesh(More)
A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations(More)
A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a gener-alisation(More)
We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The(More)
A numerical study of fluid mechanics and heat transfer in a scraped surface heat exchanger with non-Newtonian power law fluids is undertaken. Numerical results are generated for 2D steady-state conditions using finite element methods. The effect of blade design and material properties, and especially the independent effects of shear thinning and heat(More)
(2009) A moving-mesh finite element method and its application to the numerical solution of phase-change problems. It is advisable to refer to the publisher's version if you intend to cite from the work. Abstract The application of a recently developed moving mesh finite element algorithm to problems with moving internal and external boundaries is(More)
This article describes a number of velocity-based moving mesh numerical methods for multidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed mul-tidimensional moving mesh finite element method based on conservation. Finite element(More)