Finite Volume Methods
نویسنده
چکیده
1. GENERAL FORM OF FINITE VOLUME METHODS We consider vertex-centered finite volume methods for solving diffusion type elliptic equation (1) −∇ · (K∇u) = f in Ω, with suitable Dirichlet or Neumann boundary conditions. Here Ω ⊂ R is a polyhedral domain (d ≥ 2), the diffusion coefficient K(x) is a d× d symmetric matrix function that is uniformly positive definite on Ω with components in L∞(Ω), and f ∈ L(Ω). We have discussed finite element methods based on the discretization of the weak formulation and finite difference methods based on the classic formulation. We shall now present finite volume methods based on the following balance equation
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