Elliptic Interface Problems
Augmented Strategies for 3D Elliptic Interface Problems with Piecewise Constant Discontinuous Coefficients.
... 3D elliptic interface problems in which the 𝛽𝛽 coefficient, the source term, the solution and its derivatives, have a discontinuity across the interface ...Poisson problems with ...
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On convergence of the immersed boundary method for elliptic interface problems
... delta functions. With suitable quadrature formulas in the integral form using the Green functions, the authors show that their approach can get expected accuracy. However, there are few theoretical proofs on the IB ...
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A stabilized coupled method and its optimal error estimates for elliptic interface problems
... In this paper, we present a stabilized coupled algorithm for solving elliptic interface problems, mainly by introducing the jump of the solutions along the interface. A framework of ...
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Accurate Gradient Computation for Elliptic Interface Problems with Discontinuous and Variable Coefficients
... related problems. For example, the boundary value problems on an irregular ...value problems on irregular domains, many challenges exist in direct discretization at the intersections between the ...
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Error estimates for an augmented method for one dimensional elliptic interface problems
... Elliptic interface problems have many important scientific and engineering ...applications. Interface problems are encountered when the computational domain involves multi-materials with ...
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Constructions of Normal Extended Functions for Elliptic Interface Problems
... In this section, we will present two typical numerical examples for normal extended functions when the interface curves are open and closed, respectively, as solving interface problem (1). In numerical ...
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Three dimensional elliptic solvers for interface problems and applications
... dimensional elliptic interface problems in which the coefficient, the source term, the solution and its derivatives, have a discontinuity across an ...the interface appear to be second order ...
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Some Advances and Applications of Immersed Interface Methods.
... matched interface and boundary (MIB) based ADI method is proposed for heat equations with a discontinuous coefficient, which is a step forward in this ...the interface which makes the ADI method less ...for ...
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Error Analysis of the Immersed Interface Method for Elliptic Problems with an Interface.
... immersed interface method for the Poisson equation with an interface and Dirichlet boundary conditions is second-order ...immersed interface method reaches second order accuracy for two-dimensional ...
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Higher-Order Cartesian Grid Based Finite Difference Methods for Elliptic Equations on Irregular Domains and Interface Problems and their Applications
... This thesis describes higher-order finite difference methods for solving elliptic equations on irregular domains with general boundary conditions and the correspond- ing elliptic interface ...
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Multiple positive solutions of singular-Laplacian problems by variational methods
... Zhang, Critical points and positive solutions of singular elliptic boundary value problems , J. del Pino, A global estimate for the gradient in a singular elliptic boundary value problem[r] ...
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Multigrid Solution of an Elliptic Fredholm Partial Integro Differential Equation with a Hilbert Schmidt Integral Operator
... For the same experiments as in Table 4, we show large speed up in com- putational time in Table 5. Further, in Figure 1, we demonstrate that the compu- tational complexity of our multigrid procedure is ( M log M ) and ...
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Extragradient methods for elliptic inverse problems and image denoising
... In this chapter, we compare the results for each method and discuss the bene- fits and potential problems of each method as well as parameter selection. We start with the Marcotte methods. Of the three methods ...
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A fast finite difference method for solving Navier-Stokes equations on irregular domains
... Our Poisson solver on irregular domains is based on the fast immersed interface methodJ. (IIM) for interface problems.[r] ...
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Hybrid Chebyshev collocation series methods for elliptic problems
... However, at the other extreme, in the case of a general linear partial differential equation with variable coefficients, it may be necessary to apply a bivariate collocation method, such[r] ...
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Analysis of the discontinuous Galerkin method for elliptic problems on surfaces
... for elliptic problems and their error analysis have been successfully applied to problems on surfaces via the intrinsic approach in Dziuk (1988) based on interpolating the surface by a triangulated ...
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A hybridizable direct discontinuous Galerkin method for elliptic problems
... In the above derivation, we have given the discretization of the local problem when the trace value u ˆ is known. However, in general, the value of u ˆ is unknown. Therefore, we need additional conditions to overcome ...
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ERROR ESTIMATE FOR SPACE-TIME DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD OF CONVECTION-DIFFUSION PROBLEM
... 2. V. Dolejší, M. Feistauer, and J. Hozman: Analysis of semi-implicit DGFEM for nonlinear convection- diffusion problems on nonconforming meshes. Preprint No. MATHknm - 2005/1. Charles University Prague, School of ...
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Multiplicity of solutions for singular semilinear elliptic equations in weighted Sobolev spaces
... eigenvalue problems of singular quasilinear el- liptic and parabolic equations in weighted Sobolev spaces, he obtained many existence results by using Galerkin ...
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Sequential and continuum bifurcations in degenerate elliptic equations
... We apply our results to non-monotone eigenvalue problems, degenerate semi-linear elliptic equations, boundary value differential-algebraic equations and fully non-linear elliptic equatio[r] ...
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