Convergence of a Multiscale Finite Element Method with Rapidly Oscillating Coefficients
Vincent Duchêne · 2006
is the linear operator, e is a small parameter, and a(x) = (ai j(x)) is symmetric and satisfies α|ξ|2 ≤ ξiai jξ j ≤ β|ξ|2, for all ξ ∈ R2 and with 0 2). We assume that Ω = (0,1)× (0,1) ∈ R2. Corollary 2. The variational problem of (1) is to seek ue ∈ H1 0 (Ω) such that a(ue,v) = f (v), ∀v ∈ H1 0 (Ω), (2)