Estimates for spline projections

Bramble, James H.; Schatz, Alfred H.

doi:10.1051/m2an/197610r200051

Cited by 18 publications

(17 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We shall introducé in this section a kernel K h as defined in [1,2], which will produce by convolution with u h and p h a new approximation to (w, /?) in V x W, the convergence of which will be (for sufficiently smooth p) twice as fast as that of (u h , p h ) to (w, p).…”

Section: The Superconvergence Estimatesmentioning

confidence: 99%

Interior and superconvergence estimates for mixed methods for second order elliptic problems

Douglas¹,

Milner²

1985

ESAIM: M2AN

View full text Add to dashboard Cite

Section: The Superconvergence Estimatesmentioning

confidence: 99%

Interior and superconvergence estimates for mixed methods for second order elliptic problems

Douglas¹,

Milner²

1985

ESAIM: M2AN

View full text Add to dashboard Cite

“…Note also that the sketch is not to scale.) Figure 1 We have now (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) ||*¿||l, -l|Velk(B.) + 2 l|V¿||LlW.…”

Section: 1)'mentioning

confidence: 99%

“…Bramble, Nitsche, and Schatz [4], Bramble and Schatz [5], Nitsche and Schatz [16], and Schatz and Wahlbin [20], [22].…”

mentioning

confidence: 99%

Untitled

1982

Math. Comp.

View full text Add to dashboard Cite

Abstract. The Hx-projection into finite element spaces based on quasi-uniform partitions of a bounded smooth domain in RN, N > 2 arbitrary, is shown to be stable in the maximum norm (or, in the case of piecewise linear or bilinear functions, almost stable). It is not assumed that the mesh-domains coincide with the basic domain.1. Introduction. Let u be a function on a bounded closed domain "31 with smooth boundary in RN, N > 2. With 0 < h < | a parameter, let % = U*£>, r," be mesh-domains partitioned into finite elements t,a, and assume temporarily that %, Ç <3l. (As will be seen in (1.6) et seq., the last restriction is easy to overcome when applying our result.) Denote by rV^tfl,,) the class of functions with essentially bounded first derivatives (in the distribution sense), and let Sh, 0 < h < \, be finite-dimensional subspaces of W¿(%,), consisting of functions x that vanish on d% and are such that jjj^ E G2(r,h).Define uh = Pu E Sh as the //'-projection of u; i.e.,

show abstract

“…Later, Scott [14] improved and generalized this result by showing that for general dimension N > 2, elliptic operators L of order 2m, and normal covering boundary conditions, IK -i4 < C(x0)h2m~s'N/2 for2m-k^s <2m-N/2, where k > 2m is the order of approximation of Sh, where C(x0) tends to infinity as x0 approaches I\ and where the Sobolev norm index í may also be negative. Results on discrete Green's functions and problems with nonsmooth right-hand sides can also be found in, e.g., [3], [5], [7], and [13].…”

mentioning

confidence: 99%