### Abstract

The development of stability problems related to classical mixed methods has recently been observed. In this study, a soil-water coupled boundary-value problem, one type of stability problem, is presented using the element-free Galerkin method (EFG method). In this soil-water coupled problem, anomalous behavior appears in the pressure field unless a stabilization technique is used. The remedy to such numerical instability has generally been to adopt a higher interpolation order for the displacements than for the pore pressure. As an alternative, however, an added stabilization term is incorporated into the equilibrium equation. The advantages of this stabilization procedure are as follows: (1) The interpolation order for the pore pressure is the same as that for the displacements. Therefore, the interpolation functions in the pore pressure field do not reduce the accuracy of the numerical results. (2) The stabilization term consists of first derivatives. The first derivatives of the interpolation functions for the EFG Method are smooth, and therefore, the solutions for pore pressure are accurate. In order to validate the above stabilization technique, some numerical results are given. It can be seen from the results that a good convergence is obtained with this stabilization term.

Original language | English |
---|---|

Pages (from-to) | 585-597 |

Number of pages | 13 |

Journal | Computers and Geotechnics |

Volume | 38 |

Issue number | 5 |

DOIs | |

Publication status | Published - Jul 2011 |

Externally published | Yes |

### Fingerprint

### Keywords

- Mesh-free method
- Soil-water coupled problem
- Stabilization procedure

### ASJC Scopus subject areas

- Computer Science Applications
- Geotechnical Engineering and Engineering Geology

### Cite this

*Computers and Geotechnics*,

*38*(5), 585-597. https://doi.org/10.1016/j.compgeo.2011.02.016

**A stabilization procedure for soil-water coupled problems using the element-free Galerkin method.** / Shibata, Toshifumi; Murakami, A.

Research output: Contribution to journal › Article

*Computers and Geotechnics*, vol. 38, no. 5, pp. 585-597. https://doi.org/10.1016/j.compgeo.2011.02.016

}

TY - JOUR

T1 - A stabilization procedure for soil-water coupled problems using the element-free Galerkin method

AU - Shibata, Toshifumi

AU - Murakami, A.

PY - 2011/7

Y1 - 2011/7

N2 - The development of stability problems related to classical mixed methods has recently been observed. In this study, a soil-water coupled boundary-value problem, one type of stability problem, is presented using the element-free Galerkin method (EFG method). In this soil-water coupled problem, anomalous behavior appears in the pressure field unless a stabilization technique is used. The remedy to such numerical instability has generally been to adopt a higher interpolation order for the displacements than for the pore pressure. As an alternative, however, an added stabilization term is incorporated into the equilibrium equation. The advantages of this stabilization procedure are as follows: (1) The interpolation order for the pore pressure is the same as that for the displacements. Therefore, the interpolation functions in the pore pressure field do not reduce the accuracy of the numerical results. (2) The stabilization term consists of first derivatives. The first derivatives of the interpolation functions for the EFG Method are smooth, and therefore, the solutions for pore pressure are accurate. In order to validate the above stabilization technique, some numerical results are given. It can be seen from the results that a good convergence is obtained with this stabilization term.

AB - The development of stability problems related to classical mixed methods has recently been observed. In this study, a soil-water coupled boundary-value problem, one type of stability problem, is presented using the element-free Galerkin method (EFG method). In this soil-water coupled problem, anomalous behavior appears in the pressure field unless a stabilization technique is used. The remedy to such numerical instability has generally been to adopt a higher interpolation order for the displacements than for the pore pressure. As an alternative, however, an added stabilization term is incorporated into the equilibrium equation. The advantages of this stabilization procedure are as follows: (1) The interpolation order for the pore pressure is the same as that for the displacements. Therefore, the interpolation functions in the pore pressure field do not reduce the accuracy of the numerical results. (2) The stabilization term consists of first derivatives. The first derivatives of the interpolation functions for the EFG Method are smooth, and therefore, the solutions for pore pressure are accurate. In order to validate the above stabilization technique, some numerical results are given. It can be seen from the results that a good convergence is obtained with this stabilization term.

KW - Mesh-free method

KW - Soil-water coupled problem

KW - Stabilization procedure

UR - http://www.scopus.com/inward/record.url?scp=79958065877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79958065877&partnerID=8YFLogxK

U2 - 10.1016/j.compgeo.2011.02.016

DO - 10.1016/j.compgeo.2011.02.016

M3 - Article

AN - SCOPUS:79958065877

VL - 38

SP - 585

EP - 597

JO - Computers and Geotechnics

JF - Computers and Geotechnics

SN - 0266-352X

IS - 5

ER -