Quadrature rules for finite element approximations of 1D nonlocal problems
Quadrature rules for finite element approximations of 1D nonlocal problems
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一维非局部问题有限元近似的求积规则
DOI：
10.1016/j.jcp.2016.01.016
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发表时间：
2016-04
影响因子：
4.1
通讯作者：
Ju, Lili
中科院分区：
文献类型：
--
作者：
Zhang, Xiaoping;Gunzburger, Max;Ju, Lili
It is well known that calculations of the entries of the stiffness matrix in the finite element approximations of nonlocal diffusion and mechanics models are often very time-consuming due to the double integration process over the domain and the singularities of the nonlocal kernel functions. In this paper, we propose some effective and accurate quadrature rules for computing these double integrals for one-dimensional nonlocal problems; in particular, for problems with highly singular kernels, the corresponding inner integrals can be first evaluated exactly in our method, and the outer one then will be approximated by some popular quadrature rules. With these quadrature rules, the assembly of the stiffness matrix in the finite element method for the nonlocal problems becomes similar to that for the classical partial differential equations and is thus quite efficient.
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