Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 17 of 17 for “"elliptic boundary value problems"”.
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Computational Methods for Sensitivity Analysis with Applications to Elliptic Boundary Value Problems
… a study of sensitivity equation methods for elliptic boundary value problems posed on parameter dependent domains. The current focus of our efforts is the construction of a rigorous mathematical framework for sensitivity analysis and the subsequent development of efficient, accurate …
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Multilevel Mesh Adaptivity for Elliptic Boundary Value Problems in two and three Space Dimensions
… solution of a general class of variational problems. Our multilevel hybrid algorithm is a combination of node movement, edge swapping and local h-refinement. The adaptive strategy used in our hybrid algorithm is based upon the construction of a hierarchy of locally optimal meshes starting …
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Discretization and round-off errors in the finite element analysis of elliptic boundary value problems and eigenvalue problems.
Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics. Thesis. 1971. Ph.D.
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Monotone and pseudomonotone operators with applications to variational problems
… to prove the existence of solutions to nonlinear elliptic boundary value problems. A well-known approach to solving nonlinear elliptic boundary value problems is to reformulate them as equations of the form A (u) = f, where A is a monotone or pseudomonotone operator from a Sobolev space to its …
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Preconditioned iterative methods on virtual shared memory machines
… derived from finite difference discretization of elliptic boundary value problems. Most of the focus of this thesis is upon how data structures affect performance of the algorithm on the KSR1. Implications for other iterative methods and preconditioners are also drawn.
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Numerical analysis of the Fokas method in two and three dimensions
This thesis considers the numerical solution to elliptic boundary value problems (BVPs) in convex domains. Specifically we look at the two-dimensional problem in a polygon, and the three dimensional problem in a polyhedron. The nature of elliptic equations means that, knowing the values of a …
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Galerkin Projections Between Finite Element Spaces
… approximating spaces when solving elliptic PDEs with Galerkin finite element methods. For nonlinear PDEs, solving the nonlinear problem with Newton's method requires an initial guess of the solution on a refined space, which can be found by interpolating the solution from a previous …
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A Class of Immersed Finite Element Spaces and Their Application to Forward and Inverse Interface Problems
… element (IFE) spaces is developed for solving elliptic boundary value problems that have interfaces. IFE spaces are finite element approximation spaces which are based upon meshes that can be independent of interfaces in the domain. Three different quadratic IFE spaces and their related …
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Application of Helmholtz/Hodge Decomposition to Finite Element Methods for Two-Dimensional Maxwell's Equations
… obtained by solving standard second order scalar elliptic boundary value problems. This new approach is illustrated by a P1 finite element method. In Chapter 5, we further extend the new approach described in Chapter 4 to the interface problem for Maxwell's equations. We use the extraction …
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A SYSTEM OF SUPERLINEAR ELLIPTIC EQUATIONS IN A CYLINDER
… of existence of positive solutions of nonlinear elliptic boundary value problems. An important way to deal with the problem is the study of a priori estimates of positive solutions. We will adapt a classical idea which was introduced by Brezis and Turner and, together with a fixed point theorem, …
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Nonlinear diffraction and refraction of regular and random waves
… it reduces the spatial dimension of the linear boundary value problem from three to two. We extend this approximation to nonlinear waves up to the second order in wave steepness, in order to simplify the inherently three-dimensional task. Assuming that the geometrical complexity is restricted to …
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High resolution algorithms for the Navier Stokes equations for generalized descretizations
… in two dimensions include solutions to elliptic boundary value problems, Ringleb’s flow, an inviscid shock reflection, a flat plate boundary layer, and a shock induced separation over a flat plate. Three dimensional results include the ONERA M6 wing. All of the unstructured grids were …
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Signal transmission in epithelial layers
… reaction-diffusion equations leads to nonlinear elliptic boundary-value problems. We take advantage of this property and develop an extension of the method of Optimal Grids for elliptic problems. We call this method Compensated Optimal Grids. We present its application and study its convergence …
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The Seiberg-Witten equations on manifolds with boundary
… the Seiberg-Witten equations on manifolds with boundary. We divide our study into three parts. In Part One, we study the Seiberg-Witten equations on a compact 3-manifold with boundary. Here, we study the solution space of these equations without imposing any boundary conditions. We show that the …
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Adaptive finite elements for viscoelastic deformation problems
… computational aspects of generating solutions to problems involving materials with fading memory, known as viscoelastic materials. Viscoelastic materials can be loosely described as those whose current stress configuration depends on their recent past. Viscoelastic constitutive laws for stress …
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Extensions of the theory of tent spaces and applications to boundary value problems
… conormal gradients of solutions to second-order elliptic systems) within weighted tent spaces and Z-spaces. We establish this classification, and as a corollary we obtain a useful characterisation of well-posedness of Regularity and Neumann problems for second-order complex-coefficient elliptic …
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Extensions of the theory of tent spaces and applications to boundary value problems
… conormal gradients of solutions to second-order elliptic systems) within weighted tent spaces and Z-spaces. We establish this classification, and as a corollary we obtain a useful characterisation of well-posedness of Regularity and Neumann problems for second-order complex-coefficient elliptic …