On the advantages and drawbacks of a posteriori error estimation for fourth-order elliptic problems
Result description
In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures for the numerical solution of biharmonic and some further fourth order elliptic problems mostly in 2D.In the hp-adaptive finite element method, there are two possibilities to assess the error of the computed solution a posteriori: to construct a classical analytical error estimate or to obtain a more accurate reference solution by the same procedure asthe approximate solution and, from it, the computational error estimate. For the lack of space, we sometimes only refer to the notation introduced in the papers quoted. The complete hypotheses and statements of the theorems presented should also be looked for there.
Keywords
finite element methodfourth-order elliptic problema posteriori error estimates
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
On the advantages and drawbacks of a posteriori error estimation for fourth-order elliptic problems
Original language description
In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures for the numerical solution of biharmonic and some further fourth order elliptic problems mostly in 2D.In the hp-adaptive finite element method, there are two possibilities to assess the error of the computed solution a posteriori: to construct a classical analytical error estimate or to obtain a more accurate reference solution by the same procedure asthe approximate solution and, from it, the computational error estimate. For the lack of space, we sometimes only refer to the notation introduced in the papers quoted. The complete hypotheses and statements of the theorems presented should also be looked for there.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
IAA100190803: The finite element method for higher dimensional problems
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Numerical Methods for differential equations, optimization, and technological problems
ISBN
978-94-007-5287-0
Number of pages of the result
14
Pages from-to
145-158
Number of pages of the book
444
Publisher name
Springer
Place of publication
Dordrecht
UT code for WoS chapter
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Basic information
Result type
C - Chapter in a specialist book
CEP
BA - General mathematics
Year of implementation
2013