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\(W^{m,2}\)-Fehlerabschätzungen für Galerkin-Näherungen schwach elliptischer quasilinearer Randwertprobleme 2m-ter Ordnung. (German) Zbl 0561.65072

For weakly elliptic quasilinear boundary value problems of order 2m in n dimensions \(W^{m,2}\)-error estimates for the Galerkin method are established, in which \(L^{\infty}\)-norms of certain derivatives of the Galerkin approximations still occur. The order of these derivatives depends on several conditions on the coefficients of the differential operator. With the help of appropriate a priori bounds for the discrete solutions asymptotic error estimates for the finite element method may be obtained from this. This procedure yields quasi-optimal results in several cases. Finally some examples are discussed.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J40 Boundary value problems for higher-order elliptic equations
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References:

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