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Showing 1 to 20 of 218 for “"Finite element methods"”.
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Immersed and Discontinuous Finite Element Methods
… elliptic problems and construct optimal immersed finite element approximations and discontinuous immersed finite element methods for the Stokes interface problem. In the first part we present an error analysis for the minimal dissipation local discontinuous Galerkin method applied to a model …
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Finite element methods for implicit solvent models
In this thesis, we develop finite element methods (FEMs) for implicit solvent models. Implicit models treat the solvent in biomolecular systems as bulk continuum and are thus computationally efficient. The Poisson-Boltzmann equation (PBE) is one important example. We design a FEM for the linear PBE …
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Ultimate load analysis using finite element methods
Thesis: B.S., Massachusetts Institute of Technology, Department of Mechanical Engineering, 1978
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Adaptive Finite Element Methods for Parameter Identification Problems
… algorithms for their solution, based on adaptive finite element methods. Since, in general, the computational effort for solving the arising optimization problems exceeds significantly the cost for a simple simulation, the question of choosing efficient (cheap) discretizations is crucial for …
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Fast finite element methods for focused ultrasound applications
… of a three-dimensional, time-domain, fast finite element solver for focused ultrasound (FUS) applications. FUS is a rapidly evolving medical technology used for tissue heating, ablation, and neuromodulation. In recent years, interest in FUS has grown significantly, especially for the …
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Nonconforming Immersed Finite Element Methods for Interface Problems
… we consider nonconforming immersed "nite element (IFE) methods and error analysis for interface problems. We "first consider the second order elliptic interface problem with a discontinuous diffusion coefficient. We propose new IFE spaces based on the nonconforming rotated Q1 "finite …
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Recovery Techniques For Finite Element Methods And Their Applications
… techniques are important post-processing methods to obtain improved approximate solutions from primary data with reasonable cost. The practical us- age of recovery techniques is not only to improve the quality of approximation, but also to provide an asymptotically exact posteriori error …
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Elbow Joint Contact Mechanics: Multibody and Finite Element Methods
… here were first, to develop subject specific finite element (FE) models of the isolated ulno-humeral joint of the elbow and validate these models against experiment measurements. Second, to develop multibody (MB) models of the same joints with the humerus cartilage represented with discrete …
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Adaptive Finite Element Methods for Rigid Particulate Flow Problems
… laws of motion). In this work, numerical methods for some prototypical situations are developed, analyzed and validated; all of them are based on the finite element method (FEM). In this context, special emphasis is given to local grid adaptation. The goal is to obtain a high accuracy and, …
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Adaptive Finite Element Methods for the Compressible Euler Equations
… Euler equations of gas dynamics. Based on this finite element method, we develop an adaptive algorithm for the efficient computation of physically relevant quantities of the solution. This includes a posteriori error estimation of the error in the computed quantity as well as adaptive mesh …
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Unified Multilevel Adaptive Finite Element Methods for Elliptic Problems
… solution which can be used with high order finite elements. The basic step of the refinement process is the bisection of a pair of triangles, which corresponds to the addition of one or more basis functions to the approximation space. An approximation of the resulting change in the solution …
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Conservation and efficiency in least squares finite element methods
… is often sought after. However, least-squares finite element methods are known to be not mass conserving when solving fluid flow problems. In this dissertation we develop mass conservative least-squares finite element methods for the Stokes and Navier-Stokes equations through the use of …
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Design, Analysis, and Application of Immersed Finite Element Methods
… consists of three studies of immersed finite element (IFE) methods for inter- face problems related to partial differential equations (PDEs) with discontinuous coefficients. These three topics together form a continuation of the research in IFE method including the extension to …
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Higher Order Immersed Finite Element Methods for Interface Problems
… a unified framework for analyzing immersed finite element methods in one spatial dimension, and we design a new geometry conforming IFE space in two dimensions with optimal approximation capabilities, alongside with applications to the elliptic interface problem and the hyperbolic interface …
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Adaptive Finite Element Methods for Optimization in Partial Differential Equations
… necessary optimality condition in form of an indefinite boundary value problem which is approximated by an adaptive Galerkin finite element method. The mesh design in the resulting reduced models is controlled by residual-based a posteriori error estimates. These are derived by duality arguments …
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Generalized finite element methods for three-dimensional crack growth simulations
… of 3-D arbitrary crack growth using the standard Finite Element Method (FEM) encounters several difficulties. The singularities at crack fronts require strongly refined finite element meshes that must fit the discontinuity surfaces while keeping the aspect ratio of the elements within acceptable …
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Design procedures for high temperature components using finite element methods
… loadings involved. Simple and then more detailed finite element modelling establishes more accurate results for so.me complicated problems. In particular the thermal loading of the kiln is found to be considerably larger than the self weight loading. Failure analysis techniques together with a …
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Finite element methods for reduction of constraints and creep analyses.
Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.
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