By Charles Hutton

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**Additional info for A Course of Mathematics. For the Use of Academies as Well as Private Tuition. Volume I (of Two)**

**Example text**

The objective is then to decompose Á into element-wise contributions. Recalling the definition of the residual, one has Á D R uh;p I zQ D F zQ h;p h;p zQ zQ B uh;p I zQ h;p zQ (17) Because F . / and B. ; / are defined as integrals over the whole computational domain , they can be h;p h;p decomposed into a sum of contributions FK . / and Find z 2 V such that BK . ; / on each element of the mesh. It follows that B v h;p ; zh;p D Q v h;p ; 8v h;p 2 U h;p (14) X h;p h;p ÁD FK zQ zQ BK uh;p I zQ zQ then it is straightforward to show from the orthogonalK X ity property that R uh;p I zh;p D 0.

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409–542. Springer, Berlin (2009) 15. : Goal-oriented error estimation and adaptivity for the finite element method. Comput. Math. Appl. 41, 735–756 (2001) 18. : On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors. Comput. Methods Appl. Mech. Eng. 176, 313–331 (1999) 19. : Computable error estimators and adaptive techniques for fluid flow problems. , Deconinck, H. ) Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics.

### A Course of Mathematics. For the Use of Academies as Well as Private Tuition. Volume I (of Two) by Charles Hutton

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