259 citations · 538 across the 14 of their papers we have counts for
14 papers
Geometry-Conforming Finite Element Methods for Interface Problems on Fitted and Unfitted Meshes
Yuanhui Lin, Tao Lin, Xu Zhang +1
We develop an arbitrary-degree geometry-conforming finite element (GC-FE) framework for two-dimensional elliptic boundary value and interface problems on curved domains. Using the…
A unified immersed finite element error analysis for one-dimensional interface problems
Slimane Adjerid, Tao Lin, Haroun Meghaichi
It has been noted that the traditional scaling argument cannot be directly applied to the error analysis of immersed finite elements (IFE) because, in general, the spaces on the re…
Error Analysis of Symmetric Linear/Bilinear Partially Penalized Immersed Finite Element Methods for Helmholtz Interface Problems
Ruchi Guo, Tao Lin, Yanping Lin +1
This article presents an error analysis of the symmetric linear/bilinear partially penalized immersed finite element (PPIFE) methods for interface problems of Helmholtz equations.…
An Enriched Immersed Finite Element Method for Interface Problems with Nonhomogeneous Jump Conditions
Slimane Adjerid, Ivo Babuska, Ruchi Guo +1
This article presents and analyzes a -degree immersed finite element (IFE) method for elliptic interface problems with nonhomogeneous jump conditions. In this method, jump…
A Trilinear Immersed Finite Element Method for Solving Elliptic Interface Problems
Ruchi Guo, Tao Lin
This article presents an immersed finite element (IFE) method for solving the typical three-dimensional second order elliptic interface problem with an interface-independent Cartes…
A Fixed Mesh Method With Immersed Finite Elements for Solving Interface Inverse Problems
Ruchi Guo, Tao Lin, Yanping Lin
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated…
Approximation Capabilities of Immersed Finite Element Spaces for Elasticity Interface Problems
Ruchi Guo, Tao Lin, Yanping Lin
We construct and analyze a group of immersed finite element (IFE) spaces formed by linear, bilinear and rotated Q1 polynomials for solving planar elasticity equation involving inte…
A Stable Weak Galerkin Finite Element Method for Stokes Problem
Tie Zhang, Tao Lin
We study the weak Galerkin finite element method for Stokes problem. A new weak Galerkin finite element velocity-pressure space pair is presented which satisfies the discrete inf-s…
Nonconforming Immersed Finite Element Spaces For Elliptic Interface Problems
Ruchi Guo, Tao Lin, Xu Zhang
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The s…
A Group of Immersed Finite Element Spaces For Elliptic Interface Problems
Ruchi Guo, Tao Lin
We present a unified framework for developing and analysing immersed finite element (IFE) spaces for solving typical elliptic interface problems with interface independent meshes.…
A nonconforming immersed finite element method for elliptic interface problems
Tao Lin, Dongwoo Sheen, Xu Zhang
A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotat…
Partially Penalized Immersed Finite Element Methods for Parabolic Interface Problems
Tao Lin, Qing Yang, Xu Zhang
We present partially penalized immersed finite element methods for solving parabolic interface problems on Cartesian meshes. Typical semi-discrete and fully discrete schemes are di…
A Priori Error Estimates for Some Discontinuous Galerkin Immersed Finite Element Methods
Tao Lin, Qing Yang, Xu Zhang
In this paper, we derive a priori error estimates for a class of interior penalty discontinuous Galerkin (DG) methods using immersed finite element (IFE) functions for a classic se…
Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems
Tao Lin, Yanping Lin, Xu Zhang
This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved…