A mathematical and computational framework for reliable real-time solution of parametrized partial differential equations

69 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A static condensation reduced basis element method: Complex problems (2013, unknown): “Here B pr M(i),j,k;0 and B du M(i),j,k;0 are RB approximation spaces — different spaces for each {m, j, k} — obtained by a standard Greedy [14] procedure.”
Reduced-basis methods for elliptic equations in sub-domains with a posteriori error bounds and adaptivity (2005, unknown): “See [13] .”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, background): “(For description of another RB-related software system, see [121].”
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples (2012, methodology): “The reduced basis [20, 21, 23, 24, 27] and the proper orthogonal decomposition (POD) [12,15, 17, 19, 28] are two techniques belonging to this second family.”
REDUCED BASIS METHOD FOR FINITE VOLUME APPROXIMATIONS OF PARAMETRIZED LINEAR EVOLUTION EQUATIONS (2008, unknown): “The general methodology for linear elliptic equations is the subject of [33], details on algorithmic aspects can be found in [32].”
Certified Real-Time Solution of Parametrized Partial Differential Equations (2005, background): “The former can be at least partially addressed by appropriate software and architectures [37]; however, the latter will in any event remain.”