6533b833fe1ef96bd129b5a9

RESEARCH PRODUCT

Guaranteed Error Bounds I

Pekka NeittaanmäkiOlli MaliSergey RepinSergey Repin

subject

Set (abstract data type)Curvilinear coordinatesContinuum mechanicsComputer scienceSimple (abstract algebra)Computational mechanicsLinear elasticityApplied mathematicsA priori and a posterioriType (model theory)

description

In Chap. 3, we discussed the main ideas of fully reliable error control methods and the corresponding numerical algorithms with the paradigm of simple elliptic type problems. This chapter is intended to show a deep connection between a posteriori estimates of the functional type and physical relations generating the problem. Also, the goal of this chapter is to consider a wider set of problems arising in various applications and explain things in terms of computational mechanics. For this purpose, we begin with a simple class of mechanical problems (straight beams) and after that consider curvilinear beams and more complicated models of continuum mechanics (linear elasticity, viscous fluids, Maxwell type problem). At the end of the chapter we consider a generalized mathematical model, which includes almost all earlier discussed problems as particular cases.

yearjournalcountryeditionlanguage
2014-01-01
https://doi.org/10.1007/978-94-007-7581-7_3