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A mollifier useful for approximations in Sobolev spaces and some applications to approximating solutions of differential equations. (English) Zbl 0257.65087

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
41A25 Rate of convergence, degree of approximation
41A15 Spline approximation
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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[1] Shmuel Agmon, Lectures on elliptic boundary value problems, Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. · Zbl 0142.37401
[2] J. H. Bramble and S. R. Hilbert, Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation, SIAM J. Numer. Anal. 7 (1970), 112 – 124. · Zbl 0201.07803 · doi:10.1137/0707006 · doi.org
[3] J. H. Bramble and S. R. Hilbert, Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. Math. 16 (1970/1971), 362 – 369. · Zbl 0214.41405 · doi:10.1007/BF02165007 · doi.org
[4] J. H. Bramble and A. H. Schatz, Least squares methods for 2\?th order elliptic boundary-value problems, Math. Comp. 25 (1971), 1 – 32. · Zbl 0216.49202
[5] Jacques L. Lions, Problèmes aux limites dans les équations aux dérivées partielles, Deuxième édition. Séminaire de Mathématiques Supérieures, No. 1 (Été, vol. 1962, Les Presses de l’Université de Montréal, Montreal, Que., 1965 (French). · Zbl 0143.14003
[6] J. Nitsche, Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens, Numer. Math. 11 (1968), 346 – 348 (German). · Zbl 0175.45801 · doi:10.1007/BF02166687 · doi.org
[7] R. S. Varga, Functional analysis and approximation theory in numerical analysis, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1971. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 3. · Zbl 0226.65064
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