Numerische Mathematik

The Levin method is a well-known technique for evaluating oscillatory integrals, which operates by solving a certain ordinary differential equation in order to construct an antiderivative of the integrand. It was long believed that this approach ...

We introduce a novel algorithm that converges to level set convex viscosity solutions of high-dimensional Hamilton–Jacobi equations. The algorithm is applicable to a broad class of curvature motion PDEs, as well as a recently developed Hamilton–...

In Bonito (J. Comput. Phys. 448:110719, 2022), a local discontinous Galerkin method was proposed for approximating the large bending of prestrained plates, and in Bonito (IMA J. Numer. Anal. 43:627-662, 2023) the numerical properties of this ...$\mathrm{}$

The aim of this work is to construct and analyze a discretization process that preserves exponential stability at the discrete level for a wave propagation problem with boundary damping when a high-order spectral finite element approximation is ...

The celebrated Johnson-Lindenstrauss lemma states that for all $\epsilon \in (0,1)$ and finite sets $X\subseteq {\mathbb{R}}^N$ with $n>1$ elements, there exists a matrix $\mathrm{\Phi }\in {\mathbb{R}}^{m\times N}$ with $m=\mathcal{O}({\epsilon }^{-2}logn)$ such that $$\begin{array}{c}\hfill {(1-\epsilon )\Vert \mathbf{x}-\mathbf{y}\Vert }_2\le {\Vert \mathrm{\Phi }\mathbf{x}-\mathrm{\Phi }\mathbf{y}\Vert }_2\le (1+\epsilon ){\Vert \mathbf{x}-\mathbf{y}\Vert }_2\forall \mathbf{x},\mathbf{y}\in X.\end{array}$$Herein we consider so-called “terminal ...${\mathbb{}}^{}$${\mathbb{}}^{}$$\mathrm{}\mathrm{}$${\mathbb{}}^{}$${\mathbb{}}^{}{\mathbb{}}^{}$$$\begin{array}{c}\hfill {\mathrm{}\mathbf{}\mathbf{}}_{\mathrm{}}{∥,,\mathbf{},,,,,\mathbf{},∥}_{\mathrm{}}\mathrm{}{\mathbf{}\mathbf{}}_{\mathrm{}}\mathbf{}\mathbf{}{\mathbb{}}^{}\end{array}$$$\mathcal{}{}^{\mathrm{}}{}^{\mathrm{}}{}_{}$${}_{}$${}_{}\stackrel{}{\mathbf{}\mathbf{}\mathbf{}\mathbf{}{}_{\mathrm{}}\mathbf{}\mathbf{}}$

In this work we establish weak convergence rates for temporal discretisations of stochastic wave equations with multiplicative noise, in particular, for the hyperbolic Anderson model. For this class of stochastic partial differential equations the ...

We study the inversion analog of the well-known Gauss algorithm for multiplying complex matrices. A simple version is ${(A+iB)}^{-1}={(A+B{A}^{-1}B)}^{-1}-i{A}^{-1}B{(A+B{A}^{-1}B)}^{-1}$ when A is invertible, which may be traced back to Frobenius but has received scant ...$$$\mathbb{}$$\mathbb{}$$$${}^{\mathrm{}}$

In this paper, we explore the convergence of the semi-discrete Scharfetter–Gummel scheme for the aggregation-diffusion equation using a variational approach. Our investigation involves obtaining a novel gradient structure for the finite volume ...

We design an operator from the infinite-dimensional Sobolev space $\mathit{H}(\text{curl})$ to its finite-dimensional subspace formed by the Nédélec piecewise polynomials on a tetrahedral mesh that has the following properties: (1) it is defined over the entire $\mathit{H}(\text{...}$${\mathit{}}^{\mathrm{}}$$\mathit{}$$\mathit{}$$\mathit{}$$\mathit{}$