نوع مقاله : مقاله پژوهشی
نویسنده
دانشگاه آزاد اسلامی واحد شیراز
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسنده [English]
In the standard finite element method, the edges of the adjacent elements are aligned to each other, and the corner of an element does not locate on the edges of another one. If this constraint violates, the mesh is called non-conforming and the use of such meshes in the finite element method requires specific techniques. In the present paper, a new method is suggested for treating non-conforming meshes. Non-conforming meshes appear generally in adaptive mesh refinement processes especially in the quadtree mesh refinement algorithm. The quadtree is a data structure with an extremely fast recursive algorithm and is used to divide a two-dimensional domain into sub-regions or elements. In the present paper, a new approach is proposed to construct the shape functions of such elements. In this method, the shape functions are considered harmonic functions and the Laplace boundary value problem is defined and its solution is used as the shape functions of the non-conforming elements. To evaluate the applicability and accuracy of the proposed method, two numerical examples are solved and the results are presented. The results show that the proposed method can be used to effectively apply the non-conforming meshes in the finite element method.
کلیدواژهها [English]
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