4.7 Article

An immersed finite element method for elliptic interface problems on surfaces

Related references

Note: Only part of the references are listed.
Article Computer Science, Interdisciplinary Applications

The local tangential lifting method for moving interface problems on surfaces with applications

Xufeng Xiao et al.

Summary: This paper presents a new numerical computational frame for solving moving interface problems on static and evolving surfaces modeled by parabolic PDEs with Dirac delta source distributions and discontinuous coefficients. The innovative local tangential lifting method and surface front tracking method are developed to track moving interfaces on surfaces. Strategies for computing geodesic curvatures of interfaces on surfaces have been developed, and numerical examples demonstrate the accuracy of the new methods. Comparisons of dendritic solidification processes in two-dimensional spaces and on surfaces are also discussed.

JOURNAL OF COMPUTATIONAL PHYSICS (2021)

Article Computer Science, Interdisciplinary Applications

A mesh-free method for interface problems using the deep learning approach

Zhongjian Wang et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2020)

Article Engineering, Multidisciplinary

A layers capturing type H-adaptive finite element method for convection-diffusion-reaction equations on surfaces

Xufeng Xiao et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2020)

Article Computer Science, Interdisciplinary Applications

A generalized finite difference method for solving elliptic interface problems

Yanan Xing et al.

MATHEMATICS AND COMPUTERS IN SIMULATION (2020)

Article Mathematics, Applied

Residual-Based a Posteriori Error Estimation for Immersed Finite Element Methods

Cuiyu He et al.

JOURNAL OF SCIENTIFIC COMPUTING (2019)

Article Mathematics, Applied

A hybridizable discontinuous Galerkin method for elliptic interface problems in the formulation of boundary integral equations

Haixia Dong et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2018)

Article Mathematics, Applied

On Geodesic Curvature Flow with Level Set Formulation Over Triangulated Surfaces

Zheng Liu et al.

JOURNAL OF SCIENTIFIC COMPUTING (2017)

Article Mathematics, Applied

Superconvergence of immersed finite element methods for interface problems

Waixiang Cao et al.

ADVANCES IN COMPUTATIONAL MATHEMATICS (2017)

Article Mathematics, Applied

Partially Penalized Immersed Finite Element Methods for Parabolic Interface Problems

Tao Lin et al.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2015)

Article Mathematics, Applied

PARTIALLY PENALIZED IMMERSED FINITE ELEMENT METHODS FOR ELLIPTIC INTERFACE PROBLEMS

Tao Lin et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2015)

Article Mathematics

Solving PDEs with radial basis functions

Bengt Fornberg et al.

ACTA NUMERICA (2015)

Article Mathematics, Applied

A stabilized finite element method for advection-diffusion equations on surfaces

Maxim A. Olshanskii et al.

IMA JOURNAL OF NUMERICAL ANALYSIS (2014)

Article Mathematics, Applied

MIB Galerkin method for elliptic interface problems

Kelin Xia et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2014)

Article Mathematics, Applied

Analysis of the discontinuous Galerkin method for elliptic problems on surfaces

Andreas Dedner et al.

IMA JOURNAL OF NUMERICAL ANALYSIS (2013)

Article Mathematics

Finite element methods for surface PDEs

Gerhard Dziuk et al.

ACTA NUMERICA (2013)

Article Computer Science, Interdisciplinary Applications

The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

Cecile Piret

JOURNAL OF COMPUTATIONAL PHYSICS (2012)

Article Computer Science, Interdisciplinary Applications

Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants

Sashikumaar Ganesan et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2012)

Article Mathematics, Applied

ROBUST EQUILIBRATED RESIDUAL ERROR ESTIMATOR FOR DIFFUSION PROBLEMS: CONFORMING ELEMENTS

Zhiqiang Cai et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2012)

Article Mathematics, Applied

AN ADAPTIVE SURFACE FINITE ELEMENT METHOD BASED ON VOLUME MESHES

Alan Demlow et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2012)

Article Engineering, Multidisciplinary

Finite element approximation of the Cahn-Hilliard equation on surfaces

Qiang Du et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2011)

Article Mathematics, Applied

Optimal convergence analysis of an immersed interface finite element method

So-Hsiang Chou et al.

ADVANCES IN COMPUTATIONAL MATHEMATICS (2010)

Article Mathematics, Applied

An h-narrow band finite-element method for elliptic equations on implicit surfaces

Klaus Deckelnick et al.

IMA JOURNAL OF NUMERICAL ANALYSIS (2010)

Article Mathematics, Applied

A finite element method for surface PDEs: matrix properties

Maxim A. Olshanskii et al.

NUMERISCHE MATHEMATIK (2010)

Article Mathematics, Applied

A finite volume method on general surfaces and its error estimates

Lili Ju et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2009)

Article Mathematics, Applied

A FINITE ELEMENT METHOD FOR ELLIPTIC EQUATIONS ON SURFACES

Maxim A. Olshanskii et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2009)

Article Computer Science, Interdisciplinary Applications

Numerical prediction of interfacial instabilities: Sharp interface method (SIM)

R. R. Nourgaliev et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2008)

Article Mathematics, Applied

Level set equations on surfaces via the Closest Point Method

Colin B. Macdonald et al.

JOURNAL OF SCIENTIFIC COMPUTING (2008)

Article Computer Science, Interdisciplinary Applications

A sharp interface method for incompressible two-phase flows

M. Sussman et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2007)

Article Computer Science, Interdisciplinary Applications

On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method

Y. C. Zhou et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2006)

Article Mathematics, Applied

An immersed finite element space and its approximation capability

Z Li et al.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2004)

Article Mathematics, Applied

New Cartesian grid methods for interface problems using the finite element formulation

ZL Li et al.

NUMERISCHE MATHEMATIK (2003)