
	Where results make sense

Topic: Discretization error

Related Topics

error correcting code

error correction

errors and residuals in statistics

Error baseball statistics

fundamental attribution error

off by one errors

The Comedy of Errors

circular error probable

Type I error

Reed Solomon error correction

bit error ratio

In the News (Fri 25 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Fast Field Solvers FAQ
		Therefore, being able to specify an arbitrary discretization of the volume of the conductors, the accuracy of the results is affected accordingly and in general is better as the discretization is refined.
		The discretization degree of the segments is specified when ConvertHenry is launched; moreover, the discretization of every face is automatically refined near the segment edges, as the charge will concentrate there because of the edge effect.
		This error can be frustrating because from the error message no hint is given on the possible cause and of course is impossible to use the resulting matrix to simulate a structure because it lacks physical meaning.
	www.fastfieldsolvers.com /faq.htm (2343 words)

	Uncertainty and Error in CFD Simulations
		Errors in the modeling of the fluids or solids problem are concerned with the choice of the governing equations which are solved and models for the fluid or solid properties.
		Discretization errors are those errors that occur from the representation of the governing flow equations and other physical models as algebraic expressions in a discrete domain of space (finite-difference, finite-volume, finite-element) and time.
		Discretization errors are of major concern because they are dependent on the quality of the grid; however, it is often difficult to precisely indicate the relationship between a quality grid and an accurate solution prior to beginning the simulation.
	www.grc.nasa.gov /WWW/wind/valid/tutorial/errors.html (1622 words)

	EPA - 17.2 Error Messages
		When using internal gages in the watershed discretization, having gages in close proximity to one another is a known cause of problems with the watershed discretization.
		This error occurs when the soil theme used in the land cover and soils parameterization does not completely contain the watershed that is being parameterized.
		When this error message appears, it could be a result of a hole in the soils coverage or because the soil coverage boundary doesn't extend beyond the watershed boundary.
	www.epa.gov /esd/land-sci/agwa/manual/17troubleshooting/error.htm (1486 words)

	How to find errors in finite-element models
		This is analogous to ensuring the discretization errors are small by showing that the data of interest are not sensitive to discretization (results do not significantly change with finer mesh or greater p value).
		Modeling errors are not even considered in most cases because of the usual tight time constraints on analysis and a high level of expertise needed for properly executing the necessary computations.
		To properly evaluate and interpret results of an experiment, the errors of discretization must be smaller than the errors in experimental observations and the magnitude of discretization errors must be verified independently by the experiment.
	www.machinedesign.com /BDE/cadcam/bdecad3/bdecad3_6.html (3108 words)

	cm conference abstract: Boris Lastdrager, Barry Koren and Jan Verwer
		The discretization errors are present in the semi-coarsened solutions due to spatial and temporal discretization.
		Error analysis for function representation by the sparse-grid combination technique is a report on the representation error by the first two authors.
		term from the expansion of the discretization error on the semi-coarsened grids by choosing a suitable spatial discretization.
	www.mgnet.org /mgnet/conferences/CopperMtn99/abs/lastdrager.html (860 words)

	Nilesh Billade - Webpage
		In the numerical approximation of hierarchical models of thin bodies, there are two separate contributions to the total error: (a) Modeling error is the error due to dimensional reduction, and (b) Discretization error is the error due to the numerical approximation.
		Recently, a new class of finite element error estimation techniques has emerged wherein errors in a simulation are measured not in norms but in quantities of interest to the analyst.
		The modeling and the discretization errors are brought to within preset tolerance in 3 iterative steps.
	www.eng.uc.edu /~nbillade/research.html (926 words)

	RPI SCOREC - Adaptive Methods for Partial Differential Equations
		A posteriori error estimation is one method of approximating the discretization error present in a finite element solution.
		A subsequent finite element analysis and error estimation is then performed to approximate the discretization error in the refined mesh.
		In the case of h-version adaptivity the determination of the appropriate element sizes in the new discretization is based on the premise that the most efficient mesh for a given problem is the one that equally distributes the error among the elements.
	www.scorec.rpi.edu /research_adaptive.html (1161 words)

	A posteriori error estimation and adaptive mesh refinement for reliable finite element solutions
		The discretization error, that is, the difference between the exact and the FE solution, is the result of modelling a continuum with a computational model that has a finite number of degrees of freedom.
		Since the process of estimating errors in the solution and mesh refinement technique is based on a starting mesh and its FE solution, this way of estimating errors is known as a posteriori error estimation.
		The importance of error analysis is relevant in the current context as a number of decisions are being made on the basis of FEA.
	www.ias.ac.in /currsci/nov25/articles21.htm (2839 words)

	On the Global Error of Discretization Methods for Ordinary Differential Equations (Site not responding. Last check: 2007-09-16)
		Discretization methods for ordinary differential equations are usually not exact; they commit an error at every step of the algorithm.
		All these errors combine to form the global error, which is the error in the final result.
		Three different approaches are followed: to combine the effects of the errors committed at every step, to expand the global error in an asymptotic series in the step size, and to use the theory of modified equations.
	www.ma.hw.ac.uk /~jitse/phd_thesis.html (363 words)

	Publications with abstracts
		In this paper, the structure of the global error is studied for some time discretization schemes, applied to a class of stiff initial value problems as they typically arise from the semi-discretization of parabolic initial/boundary value problems (method of lines).
		Within the convergence theory of discretization methods, the existence of asymptotic error expansions in powers of the stepsize $h$ is the classical prerequisite for the theoretical justification of stepsize control mechanisms and acceleration techniques like extrapolation or defect correction.
		The estimate for the global error of an approximation obtained by collocation with piecewise polynomial functions is based on the defect correction principle.
	www.math.tuwien.ac.at /~winfried/pubmit.html (7448 words)

	The Eight-Node Hexahedral "Brick" Element in Finite Element Analysis
		FEA is a discretization technique that provides approximate answers to a physical system described in terms of a mathematical model, which is usually a system of partial differential equations (PDEs).
		“Discretization” is a method that approximates a physical system that has an infinite number of degrees of freedom, using a model that allows only finite degrees of freedom.
		One cannot really compare the discretization error of a single eight-node hexahedral element and a single four-node tetrahedral element, since the solution cost is directly proportional to the number of nodes.
	www.algor.com /news_pub/tech_white_papers/eight_node/?print=yes (1523 words)

	Property Prediction-Computation of linear elastic properties from microtomographic images: Methodology and agreement ...
		In order to obtain accurate numerical results it is necessary to estimate and minimize three sources of error: finite size effects, statistical fluctuations and discretization errors.
		In the previous section, we argued that at the length scale of voxels the averaging of the porosity is acceptable.
		Finally, we consider the discretization error; the error due to the use of discrete voxels to represent continuum objects.
	ciks.cbt.nist.gov /~garbocz/geo/node5.html (727 words)

	Accuracy
		Normally, round-off error is not considered in the numerical analysis of the algorithm, since it depends on the computer on which the algorithm is implemented, and thus is external to the numerical algorithm.
		Truncation error is present even with infinite-precision arithmetic, because it is caused by truncation of the infinite Taylor series to form the algorithm.
		Local error is the error introduced in a single step of the integration routine, while global error is the overall error caused by repeated application of the integration formula.
	lec.ugr.es /~julyan/papers/rkpaper/node3.html (994 words)

	Examining Spatial (Grid) Convergence
		The examination of the spatial convergence of a simulation is a straight-forward method for determining the ordered discretization error in a CFD simulation.
		As the grid is refined (grid cells become smaller and the number of cells in the flow domain increase) and the time step is refined (reduced) the spatial and temporal discretization errors, respectively, should asymptotically approaches zero, excluding computer round-off error.
		A general discussion of errors in CFD computations is available for background.
	www.grc.nasa.gov /WWW/wind/valid/tutorial/spatconv.html (2858 words)

	Numerical analysis (Site not responding. Last check: 2007-09-16)
		Round-off errors arise because it is impossible to represent all real numbers exactly on a finite-state machine (which is what all practical digital computers are).
		Truncation errors are committed when an iterative method is terminated and the approximate solution differs from the exact solution.
		Similarly, discretization induces a discretization error because the solution of the discrete problem does not coincide with the solution of the continuous problem.
	numerical-analysis.iqnaut.net (1576 words)

	Project-Team - smash (Site not responding. Last check: 2007-09-16)
		Once getting the fully discrete system resulting from some discretization scheme to the full set of PDE's defining the mathematical model, we face up now the issue of choosing the adequate discrete solver for large algebraic systems which are generally not linear.
		That therefore means that the solution cost of the finest level discrete system of algebraic equations up to the order of finest level discretization error is directly proportional to the total number of degrees of freedom of that finest level.
		This means that we are interested in either agglomerating or reconstruction techniques (geometrical definition of the grid levels) or algebraic techniques (the algebraic definition of the discrete coarser level residual problem is directly defined from the discrete fine level algebraic operators).
	www.inria.fr /rapportsactivite/RA2003/smash2003/module5.html (373 words)

	CS137: Introduction to Scientific Computing
		For any step size, the error in the computed solution is the global discretization error that is discussed in the text.
		Consistency means that the local discretization error (also discussed in the text) tends to zero as the step size tends to zero.
		The local discretization error for a given method can be obtained by substituting the exact solution into the method.
	www.stanford.edu /~lambers/cs137/announce1022.html (1048 words)

	Simple Web Page
		A posteriori error estimate by recovered gradients in the parabolic finite element equation (PDF).
		The theory from the elliptic case as to when such estimates are asymptotically exact, on an element, is carried over to the error on an element at a given time.
		The basic principle is that the time-step error needs to be smaller than the space-discretization error.
	www.caam.rice.edu /~dmitriy (195 words)

	Control constraints (Site not responding. Last check: 2007-09-16)
		As a consequence, standard error estimates are not suitable in the case where the inequality constraint is active.
		We expect that besides the classical a posteriori errors associated with the state and adjoint equations (5.6a) and (5.6b), respectively, the system (5.6d) becomes important.
		The error due to the discretization in space is considered as a perturbation of the error in time and incorporated by residual type a posteriori error estimators applied to the elliptic type problems resulting from the implicit time discretization.
	scicomp.math.uni-augsburg.de /german/NSF/NSFOpt/node3.html (1326 words)

	Discretization techniques
		The most straightforward way to discretize a continuous field, such as concentration of a chemical, is to evaluate it at finite number of distinct locations called grid points.
		This is a particularly intuitive way to discretize the concentration field, since we can then formulate the model in terms of the amount of the concentrate, or inventory, in each control volume, and its budget.
		Finite element discretization is particularly well-suited to unstructured grids, and is a very popular approach in these cases where the geometry is too complicated for a structured grid.
	www.ocean.washington.edu /people/faculty/kawase/NumericalModeling/Lecture_3_Slide_1.html (632 words)

	Methodologies for Treating Model Uncertainty and Discretization Error in Modeling and Simulation of Physical Systems by ...
		Furthermore, established methods for estimating certain sources of model error, such as that due to discretization, are often neglected in validation and prediction studies.
		Some sources of error, such as the effect of discretizing partial differential equations, can be modeled in an explicit non probabilistic fashion.
		In such cases, it can be more effective to model the error as a worst case bias of some assumed magnitude, and then estimate the effects of this bias on the uncertainty analysis.
	www.ima.umn.edu /reactive/abstract/alvin1.html (624 words)

	Quantization error - Wikipedia, the free encyclopedia
		When converting from an analog signal to a digital signal, error is unavoidable.
		An analog signal is continuous, with ideally infinite accuracy, while the digital signal's accuracy is dependent on the quantization resolution, or number of bits of the analog to digital converter.
		This is a different manifestation of "quantization error," in which theoretical models may be analog but physics occurs digitally.
	en.wikipedia.org /wiki/Quantization_error (208 words)

	2.1 Numerical Solution Methods (Site not responding. Last check: 2007-09-16)
		There are two measures of discretization error commonly used in discussing the accuracy of numerical methods for solving IVPs.
		Even though this is the error in which we are usually interested, it is a relatively difficult and expensive to estimate.
		Control of local error controls global error indirectly; this, of course, depends on the stability of the problem itself.
	www.phy.ornl.gov /csep/CSEP/ODE/NODE4A.html (159 words)

	UCES Methods and Analysis Chap. 2.4: Initial Value Problems - Euler's Method
		There are two types of errors: the discretization and accumulation errors.
		The tabulated errors were the largest values of all the points in time.
		Use (5) and the arguments similar to those leading to the discretization error, to derive the accumulation error estimate in the theorem.
	www.krellinst.org /UCES/archive/classes/CNA/dir2.4/uces2.4.html (1411 words)

	Title page for ETD etd-41098-234722
		The stress error indicator introduced is found to be more reliable and to converge faster than the error indicator measured in an energy norm called the residual method.
		Agreement of the calculated stress error values and the stress error indicator values confirms the convergence of final stresses to the analyst.
		The error order of the stress error estimate is postulated to be one order higher than the error order of the error estimate using the residual method.
	scholar.lib.vt.edu /theses/available/etd-41098-234722 (404 words)

	Calendar - Week of 28 November, 2004 (Site not responding. Last check: 2007-09-16)
		A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated.
		We show, theoretically and numerically, that the discretization error of the standard FEM is sensitive to the perturbation of the grid points in the region where the solution is smooth.
		We have carefully designed a special streamline diffusion finite element method whose discretization error is shown to be uniformly governed by the interpolation error in maximum norm.
	cgis.cs.umd.edu /perlcal-cgi/cal_make.pl?p1=WEE20041128 (913 words)

	No Title (Site not responding. Last check: 2007-09-16)
		In the case of finite element discretization, known mainly from solid mechanics, the physical domain is discretized in small elements.
		The discretization error in node i,j,k is defined as
		Numerical experiments (trial and error) have shown that it is sufficient for maintaining stability to compute the damping terms in the first stage of the R-K procedure, and to keep it in all the subsequent stages constant, saving substantial amount of computational time.
	www.epcc.ed.ac.uk /computing/training/document_archive/CFD (4549 words)

	OhioLINK ETD: BILLADE, NILESH
		In this work, modeling error estimates in local quantities of interest are first obtained for scalar elliptic boundary value problems posed over thin curvilinear geometries, like arches and shells, by ignoring the presence of the discretization error.
		Next, independent estimates are obtained for the modeling and discretization errors in quantities of interest for dimensionally reduced hierarchical models of thin elastic structures.
		These local estimates are used to develop what are known as goal-oriented adaptive modeling strategies in which the two errors are controlled independently to effectively reduce the total error in the quantities of interest.
	www.ohiolink.edu /etd/view.cgi?ucin1085691003 (315 words)

Try your search on: Qwika (all wikis)