Finite Element Methods: Session-#1

در اولین جلسه حضوری درس روش عناصر محدود، پیرامون مباحث ذیل مطالبی عرضه گردید: What is the finite element method? The finite element method is a numerical analysis technique for obtaining approximate solutions for a wide variety of engineering problems governed by either algebraic, ordinary and/or partial differential equations. Finite element versus finite difference methods- Advantages and disadvantages: Compared to finite element method, finite difference methods suffers from several disadvantages including: Finite difference methods work on strong form while that of finite element methods works on weak or weighted-integral form. In class, several advantages were stated for weak form compared to strong form. The flexibility in mesh generation, to capture the physical domain, will be much more easier for finite element compared to finite difference method. In a sense, finite difference methods would not be capable of employing nonuniform and non- rectangular meshes; Finite difference methods have difficulty accurately representing geometrically complex physical domain. Finite difference methods have difficulty imposing the boundary conditions along the curved boundaries; With respect to the nature of governing equation, the finite element approach differs. For algebraic equations, the direct approach or physical interpretation will be applicable; For ordinary or partial differential equations with corresponding functional, variational formulation will be applicable; For ordinary or partial differential equations with no corresponding functional, the generalized formulation works.

• #تحصیلات_و_یادگیری
• #finite_element_versus_f
• #advantages_of_finite_el
• #analytical_versus_numer