posteriori error estimator

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TítuloA residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity

TítuloA residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity

According to the above, and strongly motivated by the competitive character of our augmented formulation, we now feel the need of deriving corresponding a posteriori error estimators. More precisely, the purpose of this work is to develop a residual based a posteriori error analysis for the augmented mixed finite element scheme from [10] in the case of pure Dirichlet boundary conditions. A posteriori error analyses of the traditional mixed finite element methods for the elasticity problem can be seen in [5] and the references therein. The rest of this paper is organized as follows. In Section 2 we recall from [10] the continuous and discrete augmented formulations of the corresponding boundary value problem, state the well-posedness of both schemes, and provide the associated a priori error estimate. The kernel of the present work is given by Sections 3 and 4, where we develop the residual based a posteriori error analysis. Indeed, in Section 3 we employ a suitable auxiliary problem and apply integration by parts and the local approximation properties of the Cl´ ement interpolant to derive a reliable a posteriori error estimator. In other words, the method that we use to prove reliability combines a technique utilized in mixed finite element schemes with the usual procedure applied to primal finite element methods. It is important to remark that just one of these approaches by itself would not be enough in this case. In addition, up to our knowledge, this combined analysis seems to be applied here for the first time. Next, in Section 4 we make use of inverse inequalities and the localization technique based on triangle-bubble and edge-bubble functions to show that the estimator is efficient. We remark that, because of the new Galerkin least-squares terms employed, most of the residual terms defining the error indicator are new, and hence our proof of efficiency needs to previously establish more general versions of some technical lemmas concerning inverse estimates and piecewise polynomials. Finally, several numerical results confirming reliability, efficiency, and robustness of the estimator with respect to the Poisson ratio, are provided in Section 5. In addition, the capability of the corresponding adaptive algorithm to localize the singularities and the large stress regions of the solution is also illustrated here.
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TítuloA posteriori error analysis of an augmented mixed finite element method for Darcy flow

TítuloA posteriori error analysis of an augmented mixed finite element method for Darcy flow

We develop an a posteriori error analysis of residual type of a stabilized mixed finite element method for Darcy flow. The stabilized formulation is obtained by adding to the standard dual- mixed approach suitable residual type terms arising from Darcy’s law and the mass conservation equation. We derive sufficient conditions on the stabilization parameters that guarantee that the augmented variational formulation and the corresponding Galerkin scheme are well-posed. Then, we obtain a simple a posteriori error estimator and prove that it is reliable and locally efficient. Finally, we provide several numerical experiments that illustrate the theoretical results and support the use of the corresponding adaptive algorithm in practice.
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TítuloLow cost a posteriori error estimators for an augmented mixed FEM in linear elasticity

TítuloLow cost a posteriori error estimators for an augmented mixed FEM in linear elasticity

We remark that the a posteriori error estimator ¯ θ is locally efficient in the interior elements (that is, those that do not touch the boundary). Besides, the computation of ¯ θ involves four residuals per element in the interior tri- angles, five residuals per element in the triangles with exactly one vertex on the boundary and six residuals per element in the triangles with a side on the boundary. We emphasize that ¯ θ has been derived in the two-dimensional set- ting, assuming that displacements are approximated by continuous piecewise linear finite elements. In the next section, we provide some numerical results illustrating the performance of the corresponding adaptive method, including a numerical comparison with the a posteriori error estimator proposed in [4]. 4. Numerical experiments
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TítuloA posteriori error analysis of an augmented mixed formulation in linear elasticity with mixed and Dirichlet boundary conditions

TítuloA posteriori error analysis of an augmented mixed formulation in linear elasticity with mixed and Dirichlet boundary conditions

In order to prove the efficiency of the a posteriori error estimator ˜ θ (lower bound in (3.7)), we first observe that most of the terms involved in the definition of ˜ θ are identical or very similar to those appearing in the definition of θ (see (2.13)), so that they can be bounded from above using the same techniques. We only have to bound the last term on the right hand side of (3.6). Using the Dirichlet boundary condition and a trace theorem, we obtain

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TítuloA low order mixed finite element method for a class of quasi Newtonian Stokes flows  Part II: a posteriori error analysis

TítuloA low order mixed finite element method for a class of quasi Newtonian Stokes flows Part II: a posteriori error analysis

numerical evidences for it being efficient. Then, Figs. 1 and 2 show e versus the degrees of freedom N for Examples 1 and 2. In each case the total error e of the adaptive algorithm decreases much faster than that of the uniform one. In particular, the slow convergence observed in the uniform refinement of Example 2 is considerably improved by the corresponding adaptive strategy. These facts are also emphasized by the experimental rates of convergence provided in the tables, which show that the adaptive method recovers the order of convergence guaranteed by Theorem 3.2 in [5], that is OðhÞ. Next, Figs. 3 and 4 display some intermediate meshes obtained with the refinement procedure. We remark, as expected, that the algorithm is able to recognize the neighborhood of the singular point ð2; 2Þ in both examples.
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Position Location Estimation in Ad-Hoc Networks Using a Dead Reckoning Approach-Edición Única

Position Location Estimation in Ad-Hoc Networks Using a Dead Reckoning Approach-Edición Única

ciently high SNR, the bound predicted by the CRB in (2.1) can be achieved in multipath- free channels. Thus (2.1) provides intuition about how signal parameters like duration, bandwidth, and power affect our ability to accurately estimate the TOA. For example, doubling either the transmission power or the bandwidth will cut ranging variance in half. 2.- Multipath source of error. TOA-based range errors in multipath channels can be many times greater than those caused by additive noise alone. Essentially, all late-arriving multipath components are self-interference that effectively decrease the SNR of the desired LOS signal. Rather than finding the highest peak of the cross-correlation, in the multipath channel, the receiver must find the first-arriving peak because there is no guarantee that the LOS signal will be the strongest of the arriving signals. This can be done by measuring the time that the cross-correlation first crosses a threshold. Alternatively, in template- matching, the leading edge of the crosscorrelation is matched in a least-squares (LS) sense to the leading edge of the auto-correlation (the correlation of the transmitted signal with itself) to achieve subsampling time resolutions [24]. Generally, errors in TOA estimation are caused by two problems:
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Estimaciones y aproximaciones  Error y cota de error

Estimaciones y aproximaciones Error y cota de error

Aproximación Error absoluto Aproximación Error absoluto π = 3,1 0,041592653.... < 0,1 π = 3,14 Error: 0,001592653.... < 0,01 π = 3,141 0,000592653.... < 0,001 π = 3,1416 Error: 0,00000734.... < 0,000008 Este error es menor que 8 millonésimas, lo que da una buena aproximación para 4 cifras decimales.

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Democracia y error

Democracia y error

Mientras que en una monarquía, la causa por la que el rey es conducido al trono radica en un hecho zooló- gico (al que se otorga un carácter mítico o divino), en las democracias, la decisión se hace caer en la voluntad del pueblo. El pueblo, al que se le otorga el don de ser soberano, toma, a través del voto, la decisión de elegir entre uno y otro candidato. Se le ha hecho creer que, en última instancia, gobierna (o que participa en el acto de gobernar). Puede ser (lo es, de hecho) una ilusión. Pero es una ilusión necesaria, que posee la misma fuerza que tiene, en los pueblos a los que sin razón se llama “pri- mitivos”, las creencias en el tótem y el tabú. Sin creen- cias; sin la fianza del pueblo en las imágenes y los go- bernantes, nada se puede hacer. La actual ilusión en la democracia es de orden mítico. No se crea que la demo- cracia es científica: funda el error (y el terror).
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ANÁLISIS NUMERICO

ANÁLISIS NUMERICO

Investigaciones en el campo de la elección del valor adecuado de n dan una visión considerable de la naturaleza de la aproximación de mínimos cuadrados. Cuando n = m, se produce un polinomio interpo- lador para los n + 1 puntos usados. Para valores de n < m, el ajuste de mínimos cuadrados normalmente no pasará por los puntos, y la curva se sujetará al proceso de suavizamiento. Esto tiene un valor particular cuando el método se aplica a resultados experimentales, los cuales dan valores de la función junto con errores experimentales. La desviación más pequeña debida a los errores puede dar como resultado un polinomio altamente oscilatorio que es esencialmente el reflejo de la fluctuación debida al error. Con curvas que se espera sean suaves, incluso para valores entre dos puntos, la aproximación se puede hacer dividiendo el intervalo en muchos subintervalos. Entonces en cada subintervalo se puede usar una aproxi- mación de mínimos cuadrados basada en un polinomio de orden bajo. La sección 5.9.4 de este capítulo proporciona el código Matlab para hacer un ajuste de hasta (m − 1) orden utilizando la técnica de míni- mos cuadrados.
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A posteriori error analysis of semilinear parabolic interface problems using elliptic reconstruction

A posteriori error analysis of semilinear parabolic interface problems using elliptic reconstruction

This paper investigates a residual-based L ∞ (L 2 )-norm a posteriori error estimates for semilinear parabolic interface problem in a bounded convex domain in R 2 . An appropriate adaption of elliptic reconstruction technique and the energy method play a crucial in deriving a posteriori error bounds. It is interesting to extend these results to problems in R 3 and many computational issues which need to be addressed in future. We remark that such an extension is not straightforward. However, the authors feel that the idea of universal extension results for Sobolev spaces [22] could be useful.
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20 Lee mas

Estimativo a posteriori del error en la solución de un modelo compresible tipo Stokes

Estimativo a posteriori del error en la solución de un modelo compresible tipo Stokes

El propósito de este artículo es determinar la existencia y unicidad de un modelo tipo Stokes con densidad variable, y presentar un estimativo a posteriori del error en la solución con un método de elementos nitos. La técnica adaptativa consis- te en resolver localmente un problema auxiliar para construir un estimativo del error cometido en la aproximación. Sea Ω ⊂ R n un dominio acotado con frontera

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