Numerical verification method of solutions for nonlinear elliptic and evolutional problems
نویسنده
چکیده
where Ω is a bounded domain in Rn (1 ≤ n ≤ 3), f is a nonlinear map.We use the homogeneous Sobolev space H1 0 (Ω)(≡ H1 0 ) for the solution of (1). Also some appropriate assumptions are imposed on the map f . In order to treat the problem as the finite procedure, we use a finite element subspace Sh of H1 0 with mesh size h. Denoting the inner product on L2(Ω) by (·, ·), we define the H1 0 -projection: Phφ ∈ Sh for φ ∈ H1 0 , by (∇φ −∇(Phφ),∇vh) = 0, ∀vh ∈ Sh. (2)
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