Coupling finite element method with meshless finite difference method by means of approximation constraints. (English) Zbl 1538.74136
Summary: The novel coupling technique applied to standard Finite Element and meshless Finite Difference Methods is presented in this paper. The problem domain is a priori partitioned into a set of disjoint subdomains, which are subsequently discretized using frameworks typical for the finite element method or the meshless finite difference method. The constraints problem, based on the least square approach, is established whose solution yields combinations of degrees of freedom in subdomains that determine the global approximation field, continuous in the entire domain. The constraints problem has the matrix-type form and requires solving the strongly singular system of equations. The appropriate technique is presented to find the complete solution in the form of a hyperplane in the space of degrees of freedom. The same method is applied to enforce the boundary conditions in the meshless subdomains. The proposed approach is illustrated with several 2D examples, including the standard Poisson’s problem and selected elasticity and thermo-elasticity problems. In each case, it is shown that the novel method of coupling FEM and MFDM is effective since it provides an accurate and continuous solution in the entire domain.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 74S20 | Finite difference methods applied to problems in solid mechanics |
Keywords:
finite element method; meshless finite difference method; coupling methods; constraints problem; thermo-elastic problems; error analysisReferences:
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