Oscillation in a posteriori error estimation

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 Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems

In this work an efficient approach for a-posteriori error estimation for POD-DEIM reduced nonlinear dynamical systems is introduced. The considered nonlinear systems may also include time and parameter-affine linear terms as well as parametrically dependent inputs and outputs. The reduction process involves a Galerkin projection of the full system and approximation of the system’s nonlinearity ...

Defect-based A-posteriori Error Estimation for Index-1 DAEs

A computationally efficient a posteriori error estimator is introduced and analyzed for collocation solutions to linear index-1 DAEs with properly stated leading term. The procedure is based on a modified defect correction principle, extending an established technique from the ODE context to the DAE case. We prove that the resulting error estimate is asymptotically correct, and illustrate the m...

Defect-based a-posteriori error estimation for differential-algebraic equations

Conditions (2) imply that (AD)(t) ∈ Rm×m is singular, with rank (AD)(t) ≡ n. The requirement that D(t) be constant is not a real restriction, as any such system with varying D(t) can be rewritten by introducing a new variable u(t) = D(t)x(t), resulting in a larger system of the type (1) for x̂(t) := (x(t), u(t)) with a constant matrix D̂(t) ≡ D̂, see [4]. We consider collocation solutions p(t) for...