A method is presented to accelerate numerical simulations on parabolic problems using a numerical code and a Galerkin system (obtained vía POD plus Galerkin projection) on a sequence of interspersed intervals. The lengths of these intervals are chosen according to several basic ideas that include an a priori estímate of the error of the Galerkin approximation. Several improvements are introduce...

Model-reduction techniques aim to reduce the computational complexity of simulating dynamical systems by applying a (Petrov–)Galerkin projection process that enforces dynamics evolve in low-dimensional subspace original state space. Frequently, resulting reduced-order model (ROM) violates intrinsic physical properties full-order (e.g., global conservation, Lagrangian structure, state-variable b...

For a singularly perturbed convection-diffusion problem with exponential and characteristic boundary layers on the unit square a discretisation based on layer-adapted meshes is considered. The standard Galerkin method and the local projection scheme are analysed for a general class of higher order finite elements based on local polynomial spaces lying between Pp and Qp. We will present two diff...

This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed reduced-order models associate with optimization problems characterized by a minimum-residual objective function and nonlinear equality constraints that explicitly enfo...

In this talk we suggest a new formula for the residual of Galerkin projection onto rational Krylov spaces applied to a Sylvester equation, and establish a relation to three different underlying extremal problems for rational functions. These extremal problems enable us to compare the size of the residual for the above method with that obtained by ADI. In addition, we may deduce several new a pr...

In this article we study the properties of the hyperinterpolation operator on the unit disk D in R, approximating the orthogonal projection of a function onto the family of polynomials of degree n. A bound for the norm of the hyperinterpolation operator in the space C(D) is derived. Our results then prove the uniform convergence of the hyperinterpolation approximation of functions in the class ...

A homotopic Galerkin approach to the solution of the Fokker-Planck-Kolmogorov equation is presented. It is argued that the ideal Hilbert Space to approximate the exact solution, ψ∗, is the space L2(dψ) where dψ∗ is the probability measure induced on <n by the solution ψ∗ itself. Since this space is not accessible, it is shown that given an initial approximation sufficiently close to the exact s...

Proliferation of degrees-of-freedom has plagued discontinuous Galerkin methodology from its inception over 30 years ago. This paper develops a new computational formulation that combines the advantages of discontinuous Galerkin methods with the data structure of their continuous Galerkin counterparts. The new method uses local, element-wise problems to project a continuous finite element space ...