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Numerical solution of non-linear partial differential equations on triangulated surfacesBarreira, Maria Raquel January 2009 (has links)
This work aims to solve numerically non-linear partial differential equations on surfaces, that may evolve in time, for a set of different applications. The core of all the numerical schemes is a finite element method recently introduced for triangulated surfaces. The main classes of applications under appreciation are the motion of curves on surfaces, segmentation of images painted on surfaces and the formation of Turing patterns on surfaces. For the first one, three different approaches are considered and compared: the level set method, the phase field framework and the diffusion generated motion method. The formation of patterns leads to an interesting application to the growth of tumours which is also investigated. Implementation of all numerical schemes proposed is carried out and some analysis on the convergence and stability of the approximations is presented. The finite element method has shown efficiency and great flexibility when it comes to the equations it can approximate and the surfaces it can handle.
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Navier-Stokes equations and vector advectionNeklyudov, Mikhail January 2006 (has links)
No description available.
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Finite element approximation of some nonlinear parabolic systemsNurnberg, Robert January 2003 (has links)
No description available.
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String gradient weighted moving finite elements for systems of partial differential equationsWacher, Abigail January 2004 (has links)
No description available.
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Bayesian inference for nonlinear multivariate diffusion processesGolightly, Andrew January 2006 (has links)
No description available.
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A fully implicit, fully adaptive multigrid method for multiscale phase-field modellingRosam, Jan January 2007 (has links)
No description available.
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High order timestepping for stiff semilinear partial differential equationsKassam, Aly-Khan January 2004 (has links)
No description available.
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Exponential asymptotics of Stokes lines in partial differential equationsMortimer, D. B. January 2004 (has links)
No description available.
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Asymptotical behaviour of 2D stochastic Navier-Stokes equationsLi, Yuhong January 2004 (has links)
No description available.
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Nonlinear evolutionary equations in Banach spaces with fractional time derivativeChalk, Carl January 2006 (has links)
No description available.
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