Close Search Advanced
Journals
Resources
About Us
Open Access

Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions
Preview
Add to basket

Year:    2010

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 1 : pp. 23–39

Abstract

In this paper, a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions. Simple non-body-fitted meshes are used. For homogeneous jump conditions, both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions, a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface. With such a pair of functions, the discontinuities across the interface in the solution and flux are removed; and an equivalent elasticity interface problem with homogeneous jump conditions is formulated. Numerical examples are presented to demonstrate that such methods have second order convergence.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2009.m9001

Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 1 : pp. 23–39

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Immersed interface finite element methods elasticity interface problems singularity removal homogeneous and non-homogeneous jump conditions level-set function.

  1. Immersed Finite Element Method for Interface Problems with Algebraic Multigrid Solver

    Feng, Wenqiang | He, Xiaoming | Lin, Yanping | Zhang, Xu

    Communications in Computational Physics, Vol. 15 (2014), Iss. 4 P.1045

    https://doi.org/10.4208/cicp.150313.171013s [Citations: 30]

  2. Superconvergence of unfitted Rannacher-Turek nonconforming element for elliptic interface problems

    He, Xiaoxiao | Chen, Yanping | Ji, Haifeng | Wang, Haijin

    Applied Numerical Mathematics, Vol. 203 (2024), Iss. P.32

    https://doi.org/10.1016/j.apnum.2024.05.016 [Citations: 1]

  3. A 3D immersed finite element method with non-homogeneous interface flux jump for applications in particle-in-cell simulations of plasma–lunar surface interactions

    Han, Daoru | Wang, Pu | He, Xiaoming | Lin, Tao | Wang, Joseph

    Journal of Computational Physics, Vol. 321 (2016), Iss. P.965

    https://doi.org/10.1016/j.jcp.2016.05.057 [Citations: 51]

  4. Linear and bilinear immersed finite elements for planar elasticity interface problems

    Lin, Tao | Zhang, Xu

    Journal of Computational and Applied Mathematics, Vol. 236 (2012), Iss. 18 P.4681

    https://doi.org/10.1016/j.cam.2012.03.012 [Citations: 58]

  5. An improved immersed finite element particle-in-cell method for plasma simulation

    Bai, Jinwei | Cao, Yong | Chu, Yuchuan | Zhang, Xu

    Computers & Mathematics with Applications, Vol. 75 (2018), Iss. 6 P.1887

    https://doi.org/10.1016/j.camwa.2017.08.001 [Citations: 14]

  6. Fitted meshes on an unfitted grid based on scaled boundary finite element analysis

    Suvin, V.S. | Arrutselvi, M. | Ooi, Ean Tat | Song, Chongmin | Natarajan, Sundararajan

    Engineering Analysis with Boundary Elements, Vol. 166 (2024), Iss. P.105844

    https://doi.org/10.1016/j.enganabound.2024.105844 [Citations: 0]

  7. Immersed virtual element methods for electromagnetic interface problems in three dimensions

    Cao, Shuhao | Chen, Long | Guo, Ruchi

    Mathematical Models and Methods in Applied Sciences, Vol. 33 (2023), Iss. 03 P.455

    https://doi.org/10.1142/S0218202523500112 [Citations: 7]

  8. Matched interface and boundary method for elasticity interface problems

    Wang, Bao | Xia, Kelin | Wei, Guo-Wei

    Journal of Computational and Applied Mathematics, Vol. 285 (2015), Iss. P.203

    https://doi.org/10.1016/j.cam.2015.02.005 [Citations: 18]

  9. Augmented immersed finite element methods for some elliptic partial differential equations

    Ji, Haifeng | Chen, Jinru | Li, Zhilin

    International Journal of Computer Mathematics, Vol. 93 (2016), Iss. 3 P.540

    https://doi.org/10.1080/00207160.2015.1005010 [Citations: 3]

  10. A generalized finite difference method for solving elasticity interface problems

    Xing, Yanan | Song, Lina | Fan, Chia-Ming

    Engineering Analysis with Boundary Elements, Vol. 128 (2021), Iss. P.105

    https://doi.org/10.1016/j.enganabound.2021.03.026 [Citations: 6]

  11. A Conforming Discontinuous Galerkin Finite Element Method for Linear Elasticity Interface Problems

    Wang, Yue | Gao, Fuzheng | Cui, Jintao

    Journal of Scientific Computing, Vol. 92 (2022), Iss. 1

    https://doi.org/10.1007/s10915-022-01857-0 [Citations: 1]

  12. Long‐time stability and asymptotic analysis of the IFE method for the multilayer porous wall model

    Zhang, Huili | Wang, Kun

    Numerical Methods for Partial Differential Equations, Vol. 34 (2018), Iss. 2 P.419

    https://doi.org/10.1002/num.22206 [Citations: 3]

  13. Shape optimization with immersed interface finite element method

    Kaudur, Srivatsa Bhat | Patil, Mayuresh J.

    International Journal for Numerical Methods in Engineering, Vol. 123 (2022), Iss. 23 P.5907

    https://doi.org/10.1002/nme.7093 [Citations: 1]

  14. Discontinuous Galerkin immersed finite element methods for parabolic interface problems

    Yang, Qing | Zhang, Xu

    Journal of Computational and Applied Mathematics, Vol. 299 (2016), Iss. P.127

    https://doi.org/10.1016/j.cam.2015.11.020 [Citations: 21]

  15. An Unfitted Discontinuous Galerkin Method for Elliptic Interface Problems

    Wang, Qiuliang | Chen, Jinru

    Journal of Applied Mathematics, Vol. 2014 (2014), Iss. P.1

    https://doi.org/10.1155/2014/241890 [Citations: 1]

  16. Approximation capabilities of immersed finite element spaces for elasticity Interface problems

    Guo, Ruchi | Lin, Tao | Lin, Yanping

    Numerical Methods for Partial Differential Equations, Vol. 35 (2019), Iss. 3 P.1243

    https://doi.org/10.1002/num.22348 [Citations: 22]

  17. A weak Galerkin method for elasticity interface problems

    Wang, Chunmei | Zhang, Shangyou

    Journal of Computational and Applied Mathematics, Vol. 419 (2023), Iss. P.114726

    https://doi.org/10.1016/j.cam.2022.114726 [Citations: 6]

  18. Three-dimensional IFE-PIC numerical simulation of background pressure's effect on accelerator grid impingement current for ion optics

    Jian, Honghua | Chu, Yuchuan | Cao, Huijun | Cao, Yong | He, Xiaoming | Xia, Guangqing

    Vacuum, Vol. 116 (2015), Iss. P.130

    https://doi.org/10.1016/j.vacuum.2015.03.011 [Citations: 27]

  19. Anisotropic immersed finite element methods for 1D elliptic interface systems

    Zhang, Huili | Feng, Xinlong | Wang, Kun

    Numerical Methods for Partial Differential Equations, Vol. 39 (2023), Iss. 1 P.523

    https://doi.org/10.1002/num.22902 [Citations: 0]

  20. An enriched immersed finite element method for interface problems with nonhomogeneous jump conditions

    Adjerid, Slimane | Babuška, Ivo | Guo, Ruchi | Lin, Tao

    Computer Methods in Applied Mechanics and Engineering, Vol. 404 (2023), Iss. P.115770

    https://doi.org/10.1016/j.cma.2022.115770 [Citations: 14]

  21. A partially penalized P1/CR immersed finite element method for planar elasticity interface problems

    Liu, Angran | Chen, Jinru

    Numerical Methods for Partial Differential Equations, Vol. 35 (2019), Iss. 6 P.2318

    https://doi.org/10.1002/num.22416 [Citations: 2]

  22. Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems

    Lin, Tao | Lin, Yanping | Zhang, Xu

    SIAM Journal on Numerical Analysis, Vol. 53 (2015), Iss. 2 P.1121

    https://doi.org/10.1137/130912700 [Citations: 160]

  23. Corrected finite element methods on unfitted meshes for Stokes moving interface problem

    Laymuns, Genaro | Sánchez, Manuel A.

    Computers & Mathematics with Applications, Vol. 108 (2022), Iss. P.159

    https://doi.org/10.1016/j.camwa.2021.12.018 [Citations: 4]

  24. A Finite Element Method for High-Contrast Interface Problems with Error Estimates Independent of Contrast

    Guzmán, Johnny | Sánchez, Manuel A. | Sarkis, Marcus

    Journal of Scientific Computing, Vol. 73 (2017), Iss. 1 P.330

    https://doi.org/10.1007/s10915-017-0415-x [Citations: 32]

  25. Three‐dimensional immersed finite‐element method for anisotropic magnetostatic/electrostatic interface problems with nonhomogeneous flux jump

    Lu, Chang | Yang, Zhi | Bai, Jinwei | Cao, Yong | He, Xiaoming

    International Journal for Numerical Methods in Engineering, Vol. 121 (2020), Iss. 10 P.2107

    https://doi.org/10.1002/nme.6301 [Citations: 22]

  26. A locking-free immersed finite element method for planar elasticity interface problems

    Lin, Tao | Sheen, Dongwoo | Zhang, Xu

    Journal of Computational Physics, Vol. 247 (2013), Iss. P.228

    https://doi.org/10.1016/j.jcp.2013.03.053 [Citations: 59]

  27. A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems

    Qin, Fangfang | Chen, Jinru | Li, Zhilin | Cai, Mingchao

    Computers & Mathematics with Applications, Vol. 73 (2017), Iss. 3 P.404

    https://doi.org/10.1016/j.camwa.2016.11.033 [Citations: 13]

  28. A Nitsche-eXtended Finite Element Method for Distributed Optimal Control Problems of Elliptic Interface Equations

    Wang, Tao | Yang, Chaochao | Xie, Xiaoping

    Computational Methods in Applied Mathematics, Vol. 20 (2020), Iss. 2 P.379

    https://doi.org/10.1515/cmam-2018-0256 [Citations: 3]

  29. Monotone Finite Volume Schemes for Diffusion Equation with Imperfect Interface on Distorted Meshes

    Cao, Fujun | Sheng, Zhiqiang | Yuan, Guangwei

    Journal of Scientific Computing, Vol. 76 (2018), Iss. 2 P.1055

    https://doi.org/10.1007/s10915-018-0651-8 [Citations: 7]

  30. A Numerical Method for Solving 3D Elasticity Equations with Sharp-Edged Interfaces

    Wang, Liqun | Hou, Songming | Shi, Liwei

    International Journal of Partial Differential Equations, Vol. 2013 (2013), Iss. P.1

    https://doi.org/10.1155/2013/476873 [Citations: 8]

  31. Partially penalized IFE methods and convergence analysis for elasticity interface problems

    Huang, Peiqi | Li, Zhilin

    Journal of Computational and Applied Mathematics, Vol. 382 (2021), Iss. P.113059

    https://doi.org/10.1016/j.cam.2020.113059 [Citations: 4]

  32. Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage

    Hu, Zhengzheng | Haider, Mansoor A

    Advances in Applied Mathematics and Mechanics, Vol. 3 (2011), Iss. 6 P.729

    https://doi.org/10.4208/aamm.10-m1070 [Citations: 1]

  33. A Huygens immersed-finite-element particle-in-cell method for modeling plasma-surface interactions with moving interface

    Cao, Huijun | Cao, Yong | Chu, Yuchuan | He, Xiaoming | Lin, Tao

    Communications in Nonlinear Science and Numerical Simulation, Vol. 59 (2018), Iss. P.132

    https://doi.org/10.1016/j.cnsns.2017.10.015 [Citations: 16]

  34. A Coupled Multiphysics Model and a Decoupled Stabilized Finite Element Method for the Closed-Loop Geothermal System

    Abdullah Al Mahbub, Md. | He, Xiaoming | Nasu, Nasrin Jahan | Qiu, Changxin | Wang, Yifan | Zheng, Haibiao

    SIAM Journal on Scientific Computing, Vol. 42 (2020), Iss. 4 P.B951

    https://doi.org/10.1137/19M1293533 [Citations: 20]

  35. An iterative immersed finite element method for an electric potential interface problem based on given surface electric quantity

    Cao, Yong | Chu, Yuchuan | He, Xiaoming | Lin, Tao

    Journal of Computational Physics, Vol. 281 (2015), Iss. P.82

    https://doi.org/10.1016/j.jcp.2014.10.014 [Citations: 23]

  36. An interface penalty finite element method for elliptic interface problems on piecewise meshes

    He, Xiaoxiao | Deng, Weibing | Wu, Haijun

    Journal of Computational and Applied Mathematics, Vol. 367 (2020), Iss. P.112473

    https://doi.org/10.1016/j.cam.2019.112473 [Citations: 3]