Displaying similar documents to “Error estimates in the fast multipole method for scattering problems. Part 2 : truncation of the Gegenbauer series”

Error estimates in the fast multipole method for scattering problems. Part 1 : truncation of the Jacobi-Anger series

Quentin Carayol, Francis Collino (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We perform a complete study of the truncation error of the Jacobi-Anger series. This series expands every plane wave e i s ^ · v → in terms of spherical harmonics { Y ℓ , m ( s ^ ) } | m | ≤ ℓ ≤ ∞ . We consider the truncated series where the summation is performed over the ( ℓ , m ) ’s satisfying | m | ≤ ℓ ≤ L . We prove that if v = | v → | is large enough, the truncated series gives rise to an error lower than ϵ as soon as L satisfies L + 1 2 ≃ v + C W 2 3 ( K ϵ - δ v γ ) v 1 3 where W is the Lambert function and C , K , δ , γ are pure positive constants. Numerical experiments show that this asymptotic is optimal....

A comparison of some a posteriori error estimates for fourth order problems

Segeth, Karel

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A lot of papers and books analyze analytical a posteriori error estimates from the point of view of robustness, guaranteed upper bounds, global efficiency, etc. At the same time, adaptive finite element methods have acquired the principal position among algorithms for solving differential problems in many physical and technical applications. In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures...

A Posteriori Error Estimates for Finite Volume Approximations

S. Cochez-Dhondt, S. Nicaise, S. Repin (2009)

Mathematical Modelling of Natural Phenomena

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We present new a posteriori error estimates for the finite volume approximations of elliptic problems. They are obtained by applying functional a posteriori error estimates to natural extensions of the approximate solution and its flux computed by the finite volume method. The estimates give guaranteed upper bounds for the errors in terms of the primal (energy) norm, dual norm (for fluxes), and also in terms of the combined primal-dual norms. It is shown that the estimates provide sharp...

Complementarity - the way towards guaranteed error estimates

Vejchodský, Tomáš

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This paper presents a review of the complementary technique with the emphasis on computable and guaranteed upper bounds of the approximation error. For simplicity, the approach is described on a numerical solution of the Poisson problem. We derive the complementary error bounds, prove their fundamental properties, present the method of hypercircle, mention possible generalizations and show a couple of numerical examples.