Exploration of efficient reduced‐order modeling and a posteriori error estimation

Efficient A Posteriori Error Estimation for Finite Volume Methods

The propagation of error in numerical solutions of the compressible Navier-Stokes equations is examined using linearized, and adjoint linearized versions of the discrete flow solver. With the forward linearization it is possible, given a measure of the local residual error in the field, to obtain estimates of global solution error. This allows for example the computation of error estimates on p...

A-posteriori Modeling Error Estimation for Hierarchic Plate Models 1

Hierarchic plate models are dimensional reductions obtained by semidiscretization of the three-dimensional plate problem in the transverse direction and energy projection. We derive computable a-posteriori estimators for the modeling error thus incurred under the assumption that the resulting two-dimensional plate models are solved exactly. The estimators are valid for homogeneous, monoclinic m...

A posteriori error estimation for ellipti eigenproblems

A posteriori boundary element error estimation (

An a posteriori error estimator is presented for the boundary element method in a general framework. It is obtained by solving local residual problems for which a local concept is introduced to accommodate the fact that integral operators are nonlocal operators. The estimator is shown to have an upper and a lower bound by the constant multiples of the exact error in the energy norm for Symm’s a...

A Reliable and Efficient Implicit a Posteriori Error Estimation Technique for the Time Harmonic Maxwell Equations

We analyze an implicit a posteriori error indicator for the time harmonic Maxwell equations and prove that it is both reliable and locally efficient. For the derivation, we generalize some recent results concerning explicit a posteriori error estimates. In particular, we relax the divergence free constraint for the source term. We also justify the complexity of the obtained estimator.