Related papers: A stationary set method for estimating oscillatory…
In the paper, an approach for the numerical solution of stationary nonlinear Navier-Stokes equations in rotation and convective forms in a polygonal domain containing one reentrant corner on its boundary, that is, a corner greater than…
Stationary points or derivative zero crossings of a regression function correspond to points where a trend reverses, making their estimation scientifically important. Existing approaches to uncertainty quantification for stationary points…
We prove an exponential integral estimate for the quadratic partial sums of multiple Fourier series on large sets that implies some new properties of Fourier series.
We extend the classical Bernstein technique to the setting of integro-differential operators. As a consequence, we provide first and one-sided second derivative estimates for solutions to fractional equations, including some convex fully…
We establish upper and lower bounds for the number of integral points which lie within a neighbourhood of a smooth nondegenerate curve in $\mathbb{R}^n$ for $n\geq 3$. These estimates are new for $n\geq 4$, and we recover an earlier result…
A weak Galerkin (WG) finite element method for solving the stationary Stokes equations in two- or three- dimensional spaces by using discontinuous piecewise polynomials is developed and analyzed. The variational form we considered is based…
This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and…
We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures sigma (generalized spectral measures), and our focus here is on the case when the measure sigma is a singular…
In this paper we develop an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by conforming finite element method on isotropic meshes in $\mathbb{R}^d$, $d\in\{2,3\}$. The approach utilizes a new…
In this paper, we present a new approach to derive series expansions for some Gaussian processes based on harmonic analysis of their covariance function. In particular, we propose a new simple rate-optimal series expansion for fractional…
In this paper we introduce a family of stochastic gradient estimation techniques based of the perturbative expansion around the mean of the sampling distribution. We characterize the bias and variance of the resulting Taylor-corrected…
In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite element method (TraceFEM) for the spatial discretization and…
In this paper, we furnish van der Corput types estimates for oscillatory integrals with respect to a large parameter, where the phase is allowed to have a stationary point of real order and the amplitude to have an integrable singularity.…
Frequency domain Mie solutions to scattering from spheres have been used for a long time. However, deriving their transient analogue is a challenge as it involves an inverse Fourier transform of the spherical Hankel functions (and their…
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition…
We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a…
The article is devoted to the mean-square approximation of iterated Ito and Stratonovich stochastic integrals in the context of the numerical integration of Ito stochastic differential equations. The expansion of iterated Ito stochastic…
In this paper we study high order expansions of chart maps for local finite dimensional unstable manifolds of hyperbolic equilibrium solutions of scalar parabolic partial differential equations. Our approach is based on studying an…
We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric positive semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…