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A Compact Coupling Interface Method with Second-Order Gradient Approximation for Elliptic Interface Problems
We propose the Compact Coupling Interface Method, a finite difference method capable of obtaining second-order accurate approximations of not only...
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Oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions via Prüfer transformation
A class of Sturm-Liouville problems with discontinuity is studied in this paper. The oscillation properties of eigenfunctions for Sturm-Liouville...
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Multigrid Algorithm for Immersed Finite Element Discretizations of Elliptic Interface Problems
This paper is devoted to analyzing multigrid algorithm for solving elliptic interface problems discretized using the partially penalized immersed...
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A Priori Error Bounds for Parabolic Interface Problems with Measure Data
AbstractThis article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal...
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Second Order Convergence of a Modified MAC Scheme for Stokes Interface Problems
Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods...
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A weak Galerkin finite-element method for singularly perturbed convection–diffusion–reaction problems with interface
In this paper, a weak Galerkin (WG) finite-element method is developed and analyzed for singularly perturbed convection–diffusion–reaction problems...
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Immersed Virtual Element Methods for Elliptic Interface Problems in Two Dimensions
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted...
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A unified immersed finite element error analysis for one-dimensional interface problems
It has been known that the traditional scaling argument cannot be directly applied to the error analysis of immersed finite elements (IFE) because,...
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An Interface/Boundary-Unfitted EXtended HDG Method for Linear Elasticity Problems
An interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method of arbitrary order is proposed for linear elasticity...
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An adaptive immersed finite element method for linear parabolic interface problems with nonzero flux jump
We study an adaptive immersed finite element method for solving parabolic interface problems with nonzero flux jump in a two-dimensional convex...
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A new Petrov–Galerkin immersed finite element method for elliptic interface problems with non-homogeneous jump conditions
In this paper, we develop a Petrov–Galerkin immersed finite element method for solving elliptic interface problems in two and three dimensions. By...
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Adaptive Technique for Solving 1-D Interface Problems of Fractional Order
In this paper, we present a numerical technique for solving 1-D interface problems of fractional order. This technique relies on the reproducing...
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Virtual Element Methods for Optimal Control Problems Governed by Elliptic Interface Problems
A conforming Virtual Element Method along with a variational discretization concept for solving the optimization problem governed by an elliptic...
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A broken reproducing kernel method for the multiple interface problems
We propose a numerical method for the multiple interface problems in this paper. In our method, we first construct a new space and prove it to be a...
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Coupling of direct discontinuous Galerkin method and natural boundary element method for exterior interface problems with curved elements
This paper presents the coupling method of direct discontinuous Garlekin (DDG) and natural boundary element (NBE) for exterior interface problem. The...
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Dependence of Eigenvalues of Sturm–Liouville Problems with Eigenparameter-Dependent Boundary Conditions and Interface Conditions
In this paper, regular Sturm–Liouville problems with eigenparameter-dependent boundary conditions and interface conditions are investigated. We...
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An Immersed Raviart–Thomas Mixed Finite Element Method for Elliptic Interface Problems on Unfitted Meshes
This paper presents a lowest-order immersed Raviart–Thomas mixed triangular finite element method for solving elliptic interface problems on unfitted...
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A Conforming Discontinuous Galerkin Finite Element Method for Linear Elasticity Interface Problems
A new conforming discontinuous Galerkin method is studied for the linear elasticity interface problems with discontinuous coefficients and...
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Justification of Generalized Interface Conditions for Stokes–Darcy Problems
For accurate modeling and numerical simulation of free-flow and porous-medium flow systems, the correct choice of coupling conditions at the common...
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Optimal A Priori Error Estimates for Elliptic Interface Problems: Weak Galerkin Mixed Finite Element Approximations
We consider weak Galerkin mixed finite element approximations of second order elliptic equations on domains that can be described as a union of...
