1985
DOI: 10.21236/ada187871
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The Optimal Convergence Rate of the p-Version of the Finite Element Method.

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Cited by 65 publications
(116 citation statements)
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“…For |Γ D | = 0 we refer to [6] for the techniques to adjust the Dirichlet boundary conditions on elements Ω i such that |∂Ω i ∩ Γ D | = 0. We also refer to [4] for the arguments of partition of unity for homogeneous Dirichlet boundary conditions.…”
Section: The P-version Finite Element Solution In Two Dimensionsmentioning
confidence: 99%
See 1 more Smart Citation
“…For |Γ D | = 0 we refer to [6] for the techniques to adjust the Dirichlet boundary conditions on elements Ω i such that |∂Ω i ∩ Γ D | = 0. We also refer to [4] for the arguments of partition of unity for homogeneous Dirichlet boundary conditions.…”
Section: The P-version Finite Element Solution In Two Dimensionsmentioning
confidence: 99%
“…The convergence rate, given in ( [8]), is of order O(p −2γ+ ) with > 0, arbitrary. The result was sharpened in 1986 by removing (see [6,7]). Since then, the p-version of the finite element method has developed rapidly in all aspects such as approximation, solution of the resulting linear algebraic system, and applications to mechanics and engineering.…”
Section: Introductionmentioning
confidence: 99%
“…We ÿrst note that the smooth part and the remainder can be approximated at an arbitrarily high algebraic (spectral) rate by simply using the standard p version [13], over an arbitrary mesh.…”
Section: The Model Problemmentioning
confidence: 99%
“…3). There, we generalised known results from Schwab and Suri [16] to situations where solutions are not in H 1 ( ).…”
Section: Introduction and Formulation Of The Problemmentioning
confidence: 99%