Reduced-basis methods for elliptic equations in sub-domains with a posteriori error bounds and adaptivity

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Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations (2007, background): “Much current effort is thus devoted to development of (i ) a posteriori error estimation procedures and in particular rigorous error bounds for outputs of interest [121], and (ii ) effective sampling strategies in particular for higher (than one) dimensional parameter domains [33,32,97, 138 ,153].”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, background): “Much of this book is devoted to (i) recent work on rigorous a posteriori error estimation and in particular error bounds for outputs of interest [87, 89, 120], and (ii) effective sampling strategies in particular for higher (than one) dimensional parameter domains [32, 98, 134, 149].”
Reduced basis method for linear elasticity problems with many parameters (2008, background): “Other important aspects of the RB formulation are (i) the availability of an error bound theory to develop a rapid a posteriori error estimation based on residual calculations, see for example [25, 28], and (ii) the studies on a-priori convergence and error estimation, see [16, 24].”