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Semidiscrete Schemes of the Finite Element Method for Degenerate Hyperbolic Equations

“…This approach was used for parabolic equations in [15]. Following [14], we introduce a linear operator σ that maps some Hilbert space W onto V and has a linear inverse σ −1 , so that the norms · V and · W are equivalent.…”

“…2,α (Ω), then, instead of the estimate O h θ , we obtain the estimate O (h m ), since ν = 1 and α = β in this case and hence θ = m. In particular, for the one-dimensional problem with W =W (1) 2 (0, 1) and with linear elements for σ = x −α/2 , the estimate O(h) was obtained in [15] instead of the estimate O(1).…”