A posteriori error estimates in finite element acoustic analysis

Alonso, Ana; Russo, Anahí Dello; Vampa, Victoria

doi:10.1016/s0377-0427(99)00335-0

Cited by 14 publications

(17 citation statements)

References 13 publications

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“…As stated in [2], the above result can be extended to the case of Neumann boundary conditions. We now state a result which is useful in the proof of the superconvergence property.…”

Section: Eigenvalue Problemmentioning

confidence: 78%

Mixed approximation of eigenvalue problems: A superconvergence result

Gardini¹

2009

ESAIM: M2AN

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Abstract. We state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. It is known that a similar superconvergence result holds for the mixed approximation of Laplace problem; here we introduce a new proof, since the one given for the source problem cannot be generalized in a straightforward way to the eigenvalue problem. Numerical experiments confirm the superconvergence property and suggest that it also holds for the lowest order Brezzi-Douglas-Marini approximation.Mathematics Subject Classification. 65N25, 65N30, 65Q60.

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“…As stated in [2], the above result can be extended to the case of Neumann boundary conditions. We now state a result which is useful in the proof of the superconvergence property.…”

Section: Eigenvalue Problemmentioning

confidence: 78%

Mixed approximation of eigenvalue problems: A superconvergence result

Gardini¹

2009

ESAIM: M2AN

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“…where the last inequality is obtained by repeating the arguments in the proof of Theorem 3.1 in [1] (see in particular the estimate previous to (3.21) in this reference). Thus, since u = 1 λρ F ∇p because of Lemma 3.1, we conclude the proof from Theorems 2.2 and 2.4.…”

Section: Analysis Of the Enriched Crouzeix-raviart Approximationmentioning

confidence: 88%

“…where C is a constant independent of , r := min{s, t} as in Theorem 2.4 and r := min{ 1 2 , t} as in the previous lemma.…”

Section: Duality Argumentsmentioning

confidence: 99%

Accurate pressure post-process of a finite element method for elastoacoustics

et al. 2004

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This paper deals with a post-process to obtain a more accurate approximation of the fluid pressure from a finite element computation of the vibration modes of a fluid-structure coupled system. The underlying finite element method, based on a displacement formulation for both media, consists of using Raviart-Thomas elements for the fluid combined with standard continuous elements for the solid.An easy to compute post-process of the pressure is derived. The relation between this post-process and an alternative finite element approximation of the problem based on discretizing the fluid pressure by enriched CrouzeixRaviart elements is studied. Higher order estimates for the L 2 norm of the post-processed pressure are proved by exploiting this relation. As a by-product, higher order L 2 estimates for the solid displacements obtained with the original method are also proved. Member of CIC, Provincia de Buenos Aires, Argentina Member of CONICET, Argentina. Partially supported by FONDECYT 7.990.075 and FONDAP in Applied Mathematics, Chile Partially supported by FONDECYT 1.990.346 and FONDAP in Applied Mathematics, Chile 390 A. Alonso et al.

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“…Since Lemma 4.7 implies that A − A h H(div,R 2 ) → 0 as h → 0, then there exist exactly m eigenvalues of A h , µ (1) h , . .…”

Section: Lemma 46 There Exists a Positive Constant C Such Thatmentioning

confidence: 99%

“…From the mathematical point of view, the displacement formulation of the fluid acoustic vibration problem and its discretization with Raviart-Thomas elements is completely equivalent to the discretization with these elements of the mixed formulation of the spectral problem for the Laplacian (see [1,18]). Thus, our analysis also covers this more standard problem.…”

Section: Introductionmentioning

confidence: 99%

Finite element approximation of spectral acoustic problems on curved domains

Hernández

Rodrı́guez²

2004

Numerische Mathematik

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This paper deals with the finite element approximation of the displacement formulation of the spectral acoustic problem on a curved non convex two-dimensional domain . Convergence and error estimates are proved for Raviart-Thomas elements on a discrete polygonal domain h ⊂ in the framework of the abstract spectral approximation theory. Similar results have been previously proved only for polygonal domains. Numerical tests confirming the theoretical results are reported. (2000): 65N25, 65N30, 70J30 Mathematics Subject Classification

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A posteriori error estimates in finite element acoustic analysis

Cited by 14 publications

References 13 publications

Mixed approximation of eigenvalue problems: A superconvergence result

Mixed approximation of eigenvalue problems: A superconvergence result

Accurate pressure post-process of a finite element method for elastoacoustics

Finite element approximation of spectral acoustic problems on curved domains

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