By Weimin Han

ISBN-10: 0387235361

ISBN-13: 9780387235363

ISBN-10: 038723537X

ISBN-13: 9780387235370

This quantity offers a posteriori errors research for mathematical idealizations in modeling boundary price difficulties, specially these bobbing up in mechanical functions, and for numerical approximations of diverse nonlinear variational difficulties. the writer avoids giving the implications within the such a lot normal, summary shape in order that it's more straightforward for the reader to appreciate extra in actual fact the fundamental rules concerned. Many examples are integrated to teach the usefulness of the derived blunders estimates.

**Read Online or Download A Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical Approximations (Advances in Mechanics and Mathematics) PDF**

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**Extra info for A Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical Approximations (Advances in Mechanics and Mathematics)**

**Example text**

In this section, we will review some results of the finite element method. There are some basic aspects in the construction of finite element approximations. First we need a partition (or triangulation) of the domain of the differential equation into sub-domains called elements. 7. A finite element mesh define a finite element space. Finally, we choose basis functions for the finite element space. The basis functions should have small supports. For simplicity, we assume R is a two-dimensional polygonal domain.

Convergence of the method can also be achieved by using piecewise increasingly higher degree polynomials over relatively coarse finite element meshes, leading to the p-version finite element method. Detailed discussion of the p-version finite element method can be found in [146]. The p-version approximation is more efficient in areas where the solution is smooth, so it is natural to combine the ideas of the p-version and the h-version to make the finite element method very efficient on many problems.

If ai is not a node of K , then $ilK = 0. 30 We examine an example of linear elements. Assume R c IR2 is a poly onal domain, which is triangulated into triangles K , K E P h . e. e. the vertices of the lie in 12; and {ai}2Nint+l triangulation that lie on 8 0 . From each vertex ai, construct K~ as the patch of the elements K which contain ai as a vertex. ~~ associated with the node ai is a continuous function in 2,which is linear on each K and . corresponding piecewise linear function space is is non-zero only in K ~ The then X h = span{41i, 1 5 i 5 Nh}.

### A Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical Approximations (Advances in Mechanics and Mathematics) by Weimin Han

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