Double greedy algorithms: reduced basis methods for transport dominated problems. (English) Zbl 1291.65339

Dahmen, Wolfgang; Plesken, Christian; Welper, Gerrit

ESAIM, Math. Model. Numer. Anal. 48, No. 3, 623-663 (2014).

The authors develop a rigorous conceptual framework to obtain practically feasible tight surrogates whose condition number \(k(R) \leq C_R/c_R\) is as close to one as possible, in particular, for problem classes for which this is currently not known. The central ingredient is the construction of computationally feasible “tight” surrogates which in turn are based on deriving a suitable well-conditioned variational formulation for the parameter dependent problem.

Reviewer: Constantin Popa (Constanţa)

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
35B30	Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs

Keywords:

tight surrogates; stable variational formulations; saddle point problems; double greedy schemes; greedy stabilization; rate-optimality; transport equations; convection-diffusion equations

Software:

rbMIT