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Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids

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Abstract. This part contains new pointwise error estimates for the finite element method for second order elliptic boundary value problems on smooth bounded domains in RN. In a sense to be discussed below these sharpen known quasi–optimal L ∞ and W 1 ∞ estimates for the error on irregular quasi–uniform meshes in that they indicate a more local d...

Abstract. This part contains new pointwise error estimates for the finite element method for second order elliptic boundary value problems on smooth bounded domains in RN. In a sense to be discussed below these sharpen known quasi–optimal L ∞ and W 1 ∞ estimates for the error on irregular quasi–uniform meshes in that they indicate a more local dependence of the error at a point on the derivatives of the solution u. We note that in general the higher order finite element spaces exhibit more local behavior than lower order spaces. As a consequence of these estimates new types of error expansions will be derived which are in the form of inequalities. These expansion inequalities are valid for large classes of finite elements defined on irregular grids in RN and have applications to superconvergence and extrapolation and a posteriori estimates. Part II of this series will contain local estimates applicable to non–smooth problems. 0. Introduction and discussion of results This is the first of a series of papers whose aim is to derive new pointwise error Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-03-13

Source:

http://www.ams.org/mcom/1998-67-223/S0025-5718-98-00959-4/S0025-5718-98-00959-4.pdf

http://www.ams.org/mcom/1998-67-223/S0025-5718-98-00959-4/S0025-5718-98-00959-4.pdf Minimize

Document Type:

text

Language:

en

DDC:

518 Numerical analysis *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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astrophysical

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The importance of nuclear masses in the

The importance of nuclear masses in the Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-01-05

Source:

http://arxiv.org/pdf/astro-ph/0607625v1.pdf

http://arxiv.org/pdf/astro-ph/0607625v1.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Contemporary Mathematics Maximum Norm Error Estimates for the Finite Element Method Allowing Highly Refined Grids

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Abstract. In this article we shall survey four papers [1,3–5], two of which ( [3, 4]) are as yet unpublished, that are concerned with global L ∞ error estimates for the finite element method for elliptic problems on plane polygonal domains. 1.

Abstract. In this article we shall survey four papers [1,3–5], two of which ( [3, 4]) are as yet unpublished, that are concerned with global L ∞ error estimates for the finite element method for elliptic problems on plane polygonal domains. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-02-07

Source:

http://www.math.hkbu.edu.hk/Adaptive04/proceedings/Schatz/max.pdf

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text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Nuclear astrophysics and nuclei far from stability

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Unstable nuclei play a critical role in a number of astrophysical scenarios and are important for our understanding of the origin of the elements. Among the most important scenarios are the r-process (Supernovae), Novae, X-ray bursters, and Superbursters. For these astrophysical events I review the open questions, recent developments in astronom...

Unstable nuclei play a critical role in a number of astrophysical scenarios and are important for our understanding of the origin of the elements. Among the most important scenarios are the r-process (Supernovae), Novae, X-ray bursters, and Superbursters. For these astrophysical events I review the open questions, recent developments in astronomy, and how nuclear physics, in particular experiments with radioactive beams, needs to contribute to find the answers. 1 The r-process The r-process is one of the major nucleosynthesis processes in the universe producing roughly half of all elements heavier than iron. The proposed scenarios for this process include (i) the neutrino-driven wind in core-collapse supernovae [1, 2], (ii) accretion onto and jets from a forming neutron star in core collapse supernovae [3], and (iii) neutron star mergers [4]. So far, all these scenarios have their merits and problems and the question of the site of the r Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-11-03

Source:

http://theory.gsi.de/hirschegg/2003/Proceedings/Schatz_35.8.34.236_SMeetHirsch03Procproc2.pdf

http://theory.gsi.de/hirschegg/2003/Proceedings/Schatz_35.8.34.236_SMeetHirsch03Procproc2.pdf Minimize

Document Type:

text

Language:

en

DDC:

520 Astronomy & allied sciences *(computed)*

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Title:

The Influence of Reaction Rates on the Final p-Abundances

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The astrophysical p-process is responsible for the origin of the proton rich nuclei,which are heavier than iron. A huge network involving thousands of reaction rates is necessary to calculate the final p-abundances. But not all rates included in the network have a strong influence on the p-nuclei abundances. The p-process was investigated using ...

The astrophysical p-process is responsible for the origin of the proton rich nuclei,which are heavier than iron. A huge network involving thousands of reaction rates is necessary to calculate the final p-abundances. But not all rates included in the network have a strong influence on the p-nuclei abundances. The p-process was investigated using a full nuclear reaction network for a type II supernovae explosion when the shock front passes through the O/Ne layer. Calculations were done with a multi-layer model adopting the seed of a pre-explosion evolution of a 25 mass star. In extensive simulations we investigated the impact of single reaction rates on the final p-abundances. The results are important for the strategy of future experiments in this field. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-06

Source:

http://arxiv.org/pdf/astro-ph/0408060v1.pdf

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text

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en

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Title:

Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part I: A smooth problem and globally quasi–uniform meshes

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Abstract. We extend results from Part I about estimating gradient errors elementwise a posteriori, given there for quadratic and higher elements, to the piecewise linear case. The key to our new result is to consider certain technical estimates for differences in the error, e(x1) − e(x2), rather than for e(x) itself. We also give a posteriori es...

Abstract. We extend results from Part I about estimating gradient errors elementwise a posteriori, given there for quadratic and higher elements, to the piecewise linear case. The key to our new result is to consider certain technical estimates for differences in the error, e(x1) − e(x2), rather than for e(x) itself. We also give a posteriori estimators for second derivatives on each element. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-02-24

Source:

http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01570-9/S0025-5718-03-01570-9.pdf

http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01570-9/S0025-5718-03-01570-9.pdf Minimize

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text

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en

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Title:

Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. I. A smooth problem and globally quasi-uniform meshes

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Abstract. A class of a posteriori estimators is studied for the error in the maximum-norm of the gradient on single elements when the finite element method is used to approximate solutions of second order elliptic problems. The meshes are unstructured and, in particular, it is not assumed that there are any known superconvergent points. The esti...

Abstract. A class of a posteriori estimators is studied for the error in the maximum-norm of the gradient on single elements when the finite element method is used to approximate solutions of second order elliptic problems. The meshes are unstructured and, in particular, it is not assumed that there are any known superconvergent points. The estimators are based on averaging operators which are approximate gradients, “recovered gradients”, which are then compared to the actual gradient of the approximation on each element. Conditions are given under which they are asympotically exact or equivalent estimators on each single element of the underlying meshes. Asymptotic exactness is accomplished by letting the approximate gradient operator average over domains that are large, in a controlled fashion to be detailed below, compared to the size of the elements. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-12-22

Source:

http://www.ams.org/mcom/2001-70-235/S0025-5718-01-01286-8/S0025-5718-01-01286-8.pdf

http://www.ams.org/mcom/2001-70-235/S0025-5718-01-01286-8/S0025-5718-01-01286-8.pdf Minimize

Document Type:

text

Language:

en

DDC:

510 Mathematics *(computed)*

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Title:

1 X-ray binaries

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X-ray binaries are among the brightest extra-solar objects in the sky and are characterized by dramatic variabilities in brightness on timescales ranging from milliseconds to months and years. Their main source of power is the gravitational energy released by matter accreted from a companion star and falling onto a neutron star or a black hole

X-ray binaries are among the brightest extra-solar objects in the sky and are characterized by dramatic variabilities in brightness on timescales ranging from milliseconds to months and years. Their main source of power is the gravitational energy released by matter accreted from a companion star and falling onto a neutron star or a black hole Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-01-05

Source:

http://arxiv.org/pdf/astro-ph/0607624v1.pdf

http://arxiv.org/pdf/astro-ph/0607624v1.pdf Minimize

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text

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en

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Preprint typeset using L ATEX style emulateapj v. 6/22/04 SENSITIVITY OF P PROCESS NUCLEOSYNTHESIS TO NUCLEAR REACTION RATES IN A 25 SOLAR MASS SUPERNOVA MODEL

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The astrophysical p process, which is responsible for the origin of the proton rich stable nuclei heavier than iron, was investigated using a full nuclear reaction network for a type II supernova explosion when the shock front passes through the O/Ne layer. Calculations were performed with a multi-layer model adopting the seed of a pre-explosion...

The astrophysical p process, which is responsible for the origin of the proton rich stable nuclei heavier than iron, was investigated using a full nuclear reaction network for a type II supernova explosion when the shock front passes through the O/Ne layer. Calculations were performed with a multi-layer model adopting the seed of a pre-explosion evolution of a 25 solar mass star. The reaction flux was calculated to determine the main reaction path and branching points responsible for synthesizing the proton rich nuclei. In order to investigate the impact of nuclear reaction rates on the predicted p-process abundances, extensive simulations with different sets of collectively and individually modified neutron-, proton-, α-capture and photodisintegration rates have been performed. These results are not only relevant to explore the nuclear physics related uncertainties in p-process calculations but are also important for identifying the strategy and planning of future experiments. Subject headings: nuclear reactions, nucleosynthesis, abundances — supernovae: general 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-01-04

Source:

http://arxiv.org/pdf/astro-ph/0608341v1.pdf

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Document Type:

text

Language:

en

DDC:

660 Chemical engineering *(computed)*

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Title:

LOCAL ENERGY ESTIMATES FOR THE FINITE ELEMENT METHOD ON SHARPLY VARYING GRIDS

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Abstract. Local energy error estimates for the finite element method for elliptic problems were originally proved in 1974 by Nitsche and Schatz. These estimates show that the local energy error may be bounded by a local approximation term, plus a global “pollution ” term that measures the influence of solution quality from outside the domain of ...

Abstract. Local energy error estimates for the finite element method for elliptic problems were originally proved in 1974 by Nitsche and Schatz. These estimates show that the local energy error may be bounded by a local approximation term, plus a global “pollution ” term that measures the influence of solution quality from outside the domain of interest and is heuristically of higher order. However, the original analysis of Nitsche and Schatz is restricted to quasi-uniform grids. We present local a priori energy estimates that are valid on shape regular grids, an assumption which allows for highly graded meshes and which much more closely matches the typical practical situation. Our chief technical innovation is an improved superapproximation result. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-04

Source:

http://arxiv.org/pdf/0808.2160v1.pdf

http://arxiv.org/pdf/0808.2160v1.pdf Minimize

Document Type:

text

Language:

en

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