Reduced basis approximation for parametrized partial differential equations
In this chapter we describe the basic ideas of reduced basis (RB) approximation methods for rapid and reliable evaluation of input-output relationships in which the output is expressed as a functional of a field variable that is the solution of an input-parametrized partial differential equation (PDE). We shall focus on linear output functionals and affinely parametrized linear elliptic coercive PDEs; however the methodology is much more generally applicable as we discuss in Sec. 18.6 at the end of this chapter. The combination with an efficient a posteriori error estimation is a key factor for RB methods to be computationally successful.
KeywordsProper Orthogonal Decomposition Posteriori Error Parameter Domain Posteriori Error Estimation Reduce Basis
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