We prove optimal bounds for the discretization error of geodesic finite elements for variational partial differential equations for functions that map into a nonlinear space. For this we first generalize the well-known Céa lemma to nonlinear function spaces. In a second step we prove optimal interpolation error estimates for pointwise interpolation by geodesic finite elements of arbitrary order...

We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our estimates hold without any restrictions on the time steps for dG with exact integration or Reynolds’ quadrature. They involve a mild restriction on the...

In previous work it is shown how to numerically improve the ESVDMOR method of Feldmann and Liu to be really applicable to linear, sparse, very large scale, and continuous-time descriptor systems. Stability and passivity preservation of this algorithm is also already proven. This work presents some steps towards a global a priori error estimation for this algorithm, which is necessary for a full...

Sediment transport constantly influences river and civil structures and the lack ofinformation about its exact amount makes management efforts less effective. Hence,achieving a proper procedure to estimate the sediment load in rivers is important. We usedsupport vector machine model to estimate the sediments of the Kakareza River in LorestanProvince and the results were compared with those obta...

We derive error bounds for the Rayleigh-Ritz method for the approximation to extremal eigenpairs of a symmetric matrix. The bounds are expressed in terms of the eigenvalues of the matrix and the angle between the subspace and the eigenvector. We also present a sharp bound.

This note describes an approach to the reduction of controllers for the normalized coprime factor robustness problem as well as the normalized problem. It is shown that a relative error approximation of a coprime factor representation of any suboptimal controller leads to a stability guarantee and an upper bound on the performance degradation when the reduced order controller is implemented. Wh...

We derive error bounds for the Rayleigh-Ritz method for the approximation to extremal eigenpairs of a symmetric matrix. The bounds are expressed in terms of the eigenvalues of the matrix and the angle between the subspace and the eigenvector. We also present a sharp bound.