Read e-book online A Posterori Error Estimation in Finite Element Analysis PDF

By Mark Ainsworth, J. Tinsley Oden

ISBN-10: 047129411X

ISBN-13: 9780471294115

An updated, one-stop reference–complete with purposes

This quantity offers the main up to date info to be had on a posteriori errors estimation for finite point approximation in mechanics and arithmetic. It emphasizes tools for elliptic boundary worth difficulties and comprises functions to incompressible move and nonlinear difficulties.

Recent years have noticeable an explosion within the examine of a posteriori blunders estimators as a result of their extraordinary effect on enhancing either accuracy and reliability in clinical computing. as a way to offer an available resource, the authors have sought to provide key rules and customary ideas on a valid mathematical footing.

Topics coated during this well timed reference contain:

  • Implicit and particular a posteriori blunders estimators
  • Recovery-based errors estimators
  • Estimators, symptoms, and hierarchic bases
  • The equilibrated residual method
  • Methodology for the comparability of estimators
  • Estimation of error in amounts of curiosity

A Posteriori blunders Estimation in Finite aspect research is a lucid and handy source for researchers in nearly any box of finite aspect tools, and for utilized mathematicians and engineers who've an curiosity in errors estimation and/or finite parts.

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Extra resources for A Posterori Error Estimation in Finite Element Analysis

Example text

It may be used to derive an explicit a posteriori error estimate as follows. 30), k = int {U K' E P : K f1 K is nonempty}. 15) and IIV - ZXVIILs(8K) < ChK2 ' VIINl(K) where hK is the diameter of the element K. 16) -lEBP Finally, thanks to the coercivity of the bilinear form over the global space V, it follows that IIviiH,(n) < Cjvi, where 1-1 denotes the energy norm for the model problem. 17) 7E8P Apart from the constant C, all of the quantities on the right-hand side can be computed explicitly from the data and the finite element approximation.

The elements form a partition of the domain, that is, it = UKEP K. 2. Each element is a triangle or convex quadrilateral contained in Q. 3. The nonempty intersection of (the closure) of each distinct pair of elements is either a single common vertex or a single common edge of both elements. The diameter of a triangle K is denoted by hK and the diameter of the largest circle that may be inscribed in K is denoted by PK. 16) PK A similar concept may be defined for a quadrilateral element through a modi- fied procedure.

106) where C is a positive constant independent of hK . Proof. First, observe that C 11: IQKI + KCK' >' 11311 -VCBK I

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A Posterori Error Estimation in Finite Element Analysis by Mark Ainsworth, J. Tinsley Oden

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