Titlebook: Numerical Approximation Methods for Elliptic Boundary Value Problems; Finite and Boundary Olaf Steinbach Textbook 2008 Springer-Verlag New

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Function Spaces,In this chapter we introduce the most important function spaces as needed for the weak formulation of boundary value problems. For a further reading we refer to [1, 103, 106].

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Approximation Methods,In this chapter we describe and analyze approximation methods to solve the variational problems for operator equations as formulated in Chapter 3. This is done by introducing conforming finite dimensional trial spaces leading to linear systems of algebraic equations.

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Variational Methods,solutions of partial differential equations by using surface and volume potentials requires the solution of boundary integral operator equations to find the complete Cauchy data. In this chapter we describe the basic tools from functional analysis which are needed to investigate the unique solvability of operator equations.

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Finite Element Methods,ted in Chapter 9. Here we will just consider finite elements of lowest order, in particular we will use piecewise linear and continuous basis functions. The stability and error analysis is imbedded in the general theory as given in Chapter 8. Some numerical examples illustrate the theoretical results.