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Showing 1 to 9 of 9 for “"Elliptic Interface Problems"”.
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Higher-Degree Immersed Finite Elements for Second-Order Elliptic Interface Problems
A wide range of applications involve interface problems. In most of the cases, mathematical modeling of these interface problems leads to partial differential equations with non-smooth or discontinuous inputs and solutions, especially across material interfaces. Different numerical methods have …
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A parallel second order Cartesian method for elliptic interface problems and its application to tumor growth model
… deals with a parallel Cartesian method to solve elliptic problems with complex interfaces and its application to elliptic irregular domain problems in the framework of a tumor growth model. This method is based on a finite differences scheme and is second order accurate in the whole domain. The …
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A robust simplex cut-cell method for adaptive high-order discretizations of aerodynamics and multi-physics problems
… demonstrated through a range of aerodynamics problems, including inviscid and laminar flows. We develop a high-order DG method with a dual-consistent output evaluation for elliptic interface problems, and extend the simplex cut-cell technique for these problems, together with a …
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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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A Linear Immersed Finite Element Space Defined by Actual Interface Curve on Triangular Meshes
… 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 interface elements are derived. Based on these geometric identities and estimates, we establish a multi-point …
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High-order hybrid methods using Green's functions and finite elements
… for linear partial differential boundary value problems by directly defining solutions in integral form. For a Green's function that satisfies the desired boundary conditions, this form is a convolution of the Green's function with the right hand side. However, straightforward numerical …
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Immersed Finite Elements for a Second Order Elliptic Operator and Their Applications
… 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 coefficient associated with the …
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Nonconforming Immersed Finite Element Methods for Interface Problems
… simulations, it usually leads to the so-called interface problems of PDEs whose coefficients are discontinuous. 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 …
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Design, Analysis, and Application of Immersed Finite Element Methods
… 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 elasticity systems, new breakthroughs to higher …