Related papers: Stable and Accurate Interpolation Operators for Hi…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
This paper presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators…
We study non-conforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a…
We construct, on continuous $Q_1$ finite elements over Cartesian meshes, an interpolation operator that does not increase the total variation. The operator is stable in $L^1$ and exhibits second order approximation properties. With the help…
We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the…
A methodology for handling block-to-block coupling of nonconforming, multiblock summation-by-parts finite difference methods is proposed. The coupling is based on the construction of projection operators that move a finite difference grid…
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…
We introduce interpolation operators with approximation and stability properties suited for parabolic problems in primal and mixed formulations. We derive localized error estimates for tensor product meshes (occurring in classical…
Finite difference schemes for the simulation of elastic waves in materi- als with jump discontinuities are presented. The key feature is the highly accurate treatment of interfaces where media discontinuities arise. The schemes are…
We prove stability bounds for Stokes-like virtual element spaces in two and three dimensions. Such bounds are also instrumental in deriving optimal interpolation estimates. Furthermore, we develop some numerical tests in order to…
Various algebraic multigrid algorithms have been developed for solving problems in scientific and engineering computation over the past decades. They have been shown to be well-suited for solving discretized partial differential equations…
The quantitative estimation for the interpolation error constants of the Fujino-Morley interpolation operator is considered. To give concrete upper bounds for the constants, which is reduced to the problem of providing lower bounds for…
This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces.This operator gives optimal estimates of the…
Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished. An equation, which can be the base equation for investigation of the…
Stochastic interpolants offer a robust framework for continuously transforming samples between arbitrary data distributions, holding significant promise for generative modeling. Despite their potential, rigorous finite-time convergence…
Efficient solution of the lowest eigenmodes is studied for a family of related eigenvalue problems with common $2\times 2$ block structure. It is assumed that the upper diagonal block varies between different versions while the lower…
In this paper, we investigate the combination of multigrid methods and neural networks, starting from a Finite Element discretization of an elliptic PDE. Multigrid methods use interpolation operators to transfer information between…
The worst-case performance of an optimization method on a problem class can be analyzed using a finite description of the problem class, known as interpolation conditions. In this work, we study interpolation conditions for linear operators…
We prove stability and interpolation estimates for Hellinger-Reissner virtual elements; the constants appearing in such estimates only depend on the aspect ratio of the polytope under consideration and the degree of accuracy of the scheme.…
High-order finite difference methods are efficient, easy to program, scales well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback have been the complicated and…