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 13 of 13 for “"Immersed finite element"”.
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Nonconforming Immersed Finite Element Methods for Interface Problems
… In this dissertation, 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 …
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Design, Analysis, and Application of Immersed Finite Element Methods
This dissertation 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
… we provide 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 …
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Immersed Finite Element Particle-In-Cell Simulations of Ion Propulsion
… new algorithm is based on the three-dimensional immersed finite element method which is developed in this thesis, and a modified legacy particle-in-cell code. The model also applies a new meshing technique that separates the field solution mesh from the particle pushing mesh in order to increase …
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A Hermite Cubic Immersed Finite Element Space for Beam Design Problems
This thesis develops an immersed finite element (IFE) space for numerical simulations arising from beam design with multiple materials. This IFE space is based upon meshes that can be independent of interface of the materials used to form a beam. Both the forward and inverse problems associated …
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Immersed Finite Element Particle-In-Cell Modeling of Surface Charging in Rarefied Plasmas
… in space plasma engineering. A three-dimensional Immersed Finite Element Particle-In-Cell (IFE-PIC) method is developed to model surface charging involving complex boundary conditions. This method extends the previous IFE-PIC algorithm to explicitly include charge deposition on a dielectric …
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A Linear Immersed Finite Element Space Defined by Actual Interface Curve on Triangular Meshes
In this thesis, we develop the a new immersed finite element(IFE) space formed by piecewise linear polynomials defined on sub-elements cut by the actual interface curve for solving elliptic interface problems on interface independent meshes. A group of geometric identities and estimates on …
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A Class of Immersed Finite Element Spaces and Their Application to Forward and Inverse Interface Problems
A class of immersed finite 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 …
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Higher-Degree Immersed Finite Elements for Second-Order Elliptic Interface Problems
… the interface. The main focus of our work is the immersed finite element method to obtain optimal numerical solutions for interface problems. In this thesis, we present piecewise quadratic immersed finite element (IFE) spaces that are used with an immersed finite element (IFE) method with interior …
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Immersed and Discontinuous Finite Element Methods
… for 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 …
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Immersed Discontinuous Galerkin Methods for Acoustic Wave Propagation in Inhomogeneous Media
We present immersed discontinuous Galerkin finite element methods for one and two dimensional acoustic wave propagation problems in inhomogeneous media where elements are allowed to be cut by the material interface. The proposed methods use the standard discontinuous Galerkin finite element …
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Immersed Finite Elements for a Second Order Elliptic Operator and Their Applications
This dissertation studies immersed finite elements (IFE) for a second order elliptic operator and their applications to interface problems of related partial differential equations. We start with the immersed finite element methods for the second order elliptic operator with a discontinuous …
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Bilinear Immersed Finite Elements For Interface Problems
In this dissertation we discuss bilinear immersed finite elements (IFE) for solving interface problems. The related research works can be categorized into three aspects: (1) the construction of the bilinear immersed finite element spaces; (2) numerical methods based on these IFE spaces for solving …