TY - JOUR

T1 - Analysis and application of the interpolating element free Galerkin (IEFG) method to simulate the prevention of groundwater contamination with application in fluid flow

AU - Abbaszadeh, Mostafa

AU - Dehghan, Mehdi

AU - Khodadadian, Amirreza

AU - Heitzinger, Clemens

N1 - Funding Information: The authors are very grateful to the reviewers for carefully reading this paper and for their comments and suggestions which improved the paper. Amirreza Khodadadian and Clemens Heitzinger acknowledge support by FWF (Austrian Science Fund) START Project No. Y660 PDE Models for Nanotechnology.

PY - 2020/4

Y1 - 2020/4

N2 - We develop a meshless numerical procedure to simulate the groundwater equation (GWE). The used technique is based on the interpolating element free Galerkin (IEFG) method. The interpolating moving least squares (IMLS) approximation produces a set of functions such that they are well-known as “shape functions”. The IEFG technique employs the shape functions of IMLS approximation. The shape functions of IMLS approximation vanish on the boundary and also they satisfy the property of the Kronecker Delta function. Thus, Dirichlet boundary conditions can be exactly imposed. In this paper, we check the unconditional stability and convergence of the proposed numerical scheme based on the energy method. The numerical results confirm the theoretical analysis.

AB - We develop a meshless numerical procedure to simulate the groundwater equation (GWE). The used technique is based on the interpolating element free Galerkin (IEFG) method. The interpolating moving least squares (IMLS) approximation produces a set of functions such that they are well-known as “shape functions”. The IEFG technique employs the shape functions of IMLS approximation. The shape functions of IMLS approximation vanish on the boundary and also they satisfy the property of the Kronecker Delta function. Thus, Dirichlet boundary conditions can be exactly imposed. In this paper, we check the unconditional stability and convergence of the proposed numerical scheme based on the energy method. The numerical results confirm the theoretical analysis.

KW - Convergence

KW - Element free Galerkin (EFG) method

KW - Groundwater equation and fluid flow

KW - Interpolating MLS

KW - Prevention of groundwater contamination

KW - Unconditionally stable

UR - http://www.scopus.com/inward/record.url?scp=85074279651&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2019.112453

DO - 10.1016/j.cam.2019.112453

M3 - Article

AN - SCOPUS:85074279651

VL - 368

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

M1 - 112453

ER -