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Zbl 0888.65117
Zhang, Tie
The stability and approximation properties of Ritz-Volterra projection and application. I.
(English)
[J] Numer. Math., J. Chin. Univ. 6, No.1, 57-76 (1997). ISSN 1004-8979

By adding an integral term to the usual bilinear form on $H^1_0\times H^1_0$ 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 $W^1_p$ and $L_p$ for $2\le p\le\infty$ also hold for the Ritz-Volterra projection. The proof is based on the Green function technique and on some related estimates.
[O.Titow (Berlin)]
MSC 2000:
*65N30 Finite numerical methods (BVP of PDE)
65N12 Stability and convergence of numerical methods (BVP of PDE)
35J25 Second order elliptic equations, boundary value problems

Keywords: Ritz projection; Ritz-Volterra projection; stability; Green function technique

Cited in: Zbl 0982.65144

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