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The stability and approximation properties of Ritz-Volterra projection and application. I. (English) Zbl 0888.65117
By adding an integral term to the usual bilinear form on H 0 1 ×H 0 1 which defines the Ritz projection, the author studies a non-classical H 1 -projection named here a Ritz-Volterra projection. The main result claims that stability and approximation properties which are valid for the Ritz projection in W p 1 and L p for 2p also hold for the Ritz-Volterra projection. The proof is based on the Green function technique and on some related estimates.
Reviewer: O.Titow (Berlin)

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
35J25Second order elliptic equations, boundary value problems