By Repin, Sergey
This publication offers with the trustworthy verification of the accuracy of approximate suggestions that is one of many imperative difficulties in sleek utilized research. After giving an summary of the equipment built for types according to partial differential equations, the writer derives computable a posteriori errors estimates through the use of tools of the speculation of partial differential equations and useful research. those estimates are acceptable to approximate recommendations computed by means of a variety of methods. Read more...
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Extra info for A posteriori estimates for partial differential equations
Zienkiewicz . They result in stress fields that satisfy an equilibrium condition in a weak form. A method of equilibration is presented in P. Destuynder and B. M´etivet . This paper also contain numerical tests, in which a posteriori error estimates obtained by equilibration are compared with other estimates. Recently a new equilibration method was suggested in publications of D. Braess and J. Sch¨oberl [67, 69]. In it fluxes are projected to a subspace formed by Raviart– Thomas elements.
W. Engl and O. Scherzer ). A further study of this strategy is presented in Jin Qi-nian and Hou Zong-yi . A posteriori estimates for linear ill-posed problems were investigated in A. Leonov . , in K. Braune , Jin Qi-nian , P. Meyer , F. Potra , K. Tsuruta and K. Ohmori , T. Yamamoto . Boundary value problems are often reformulated in terms of integral equations. , boundary element methods) are usually derived with the help of the techniques that exploits special properties of the iteration operator.
Assume that it is required to estimate the quantity h`; u uh i, where ` 2 V0 is a given linear functional. Typically, ` is an integral type functional localized in a certain part of . Define u` by the relation Z A? 32) in which A? is the matrix adjoint to A. 32), it follows that Z A? u v/i can be easily estimated provided that u` is known. In practice, u` is replaced by an approximation u` computed on an adjoint mesh T (which may not coincide with Th ). u` ; uh / could be a good indicator of h`; u uh i.
A posteriori estimates for partial differential equations by Repin, Sergey