The conforming finite element Galerkin method is applied to discretise in the spatial direction for a class of strongly nonlinear parabolic problems. Using elliptic projection associated linearised stationary problem with Gronwall type result, optimal error estimates are derived, when piecewise polynomials degree r≥1 used, which improve upon earlier results Axelsson ((1977) [3]) requiring 2d r≥...

In this contribution, an online adaptive reduced order model is presented for small-strain elasto-plasticity. Using the GALERKIN method, problem projected to a lower subspace giving based on displacement field snapshots. The adaptivity lies in update of projection operator, which carried out different parts simulation if certain criteria related convergence behavior are not fulfilled. With rela...

In the last five years, the scientific computing community has taken great interest in the so-called stochastic Galerkin schemes (SGS). These schemes are typically used to address the following type of problem: Suppose that I have a deterministic differential equation model for which I can find an approximate solution using standard numerical discretization techniques. Now suppose that, in an a...

In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying dominant subspaces based reachability Gramian a system. Once desired subspace computed, reduced order then obtained Galerkin projection. We prove that, in case, either preserves mean square asymptotic stability or leads to models w...

Data-driven reduced order models (ROMs) are combined with the Lippmann-Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as Galerkin projection and sparse due Lanczos orthogonalization. Embedding into continuous problem, data-driven internal solution produced. This then used in equation, thus making further iterative updates unnecessary. We show numer...

Approximating solutions of non-linear parametrized physical problems by interpolation presents a major challenge in terms accuracy. In fact, pointwise such is rarely efficient and generally leads to incorrect predictions. To overcome this issue, instead interpolating directly straightforward approach, reduced order models (ROMs) can be efficiently used. end, the ITSGM (Interpolation On Tangent ...