An improved error bound for reduced basis approximation of linear parabolic problems
Author(s)Urban, Karsten; Patera, Anthony T.
MetadataShow full item record
We consider a space-time variational formulation for linear parabolic partial differential equations. We introduce an associated Petrov-Galerkin truth finite element discretization with favorable discrete inf-sup constant β[subscript δ], the inverse of which enters into error estimates: β[subscript δ] is unity for the heat equation; β[subscript δ] decreases only linearly in time for non-coercive (but asymptotically stable) convection operators. The latter in turn permits effective long-time a posteriori error bounds for reduced basis approximations, in sharp contrast to classical (pessimistic) exponentially growing energy estimates. The paper contains a full analysis and various extensions for the formulation introduced briefly by Urban and Patera (2012) as well as numerical results for a model reaction-convection-diffusion equation.
DepartmentMassachusetts Institute of Technology. Department of Mechanical Engineering
Mathematics of Computation
American Mathematical Society (AMS)
Urban, Karsten, and Anthony T. Patera. “An Improved Error Bound for Reduced Basis Approximation of Linear Parabolic Problems.” Mathematics of Computation 83, no. 288 (October 23, 2013): 1599–1615. © 2013 American Mathematical Society
Final published version