SIAM Journal on Numerical Analysis

The thin plate spline smoother is a classical model for finding a smooth function from the knowledge of its observation at scattered locations which may have random noises. We consider a nonconforming Morley finite element method to approximate the ...

The mathematical foundation of the so-called extended coupled-cluster method for the solution of the many-fermion Schrödinger equation is here developed. We prove an existence and uniqueness result, both in the full infinite-dimensional amplitude space as ...

We study the numerical approximation of integrals over ${R}^s$ with respect to the standard Gaussian measure for integrands which lie in certain Hermite spaces of functions. The decay rate of the associated sequence is specified by a single integer ...

We consider the stochastic Cahn--Hilliard equation driven by additive Gaussian noise in a convex domain with polygonal boundary in dimension $d\le 3$. We discretize the equation using a standard finite element method in space and a fully implicit backward ...

In this paper, we study the superconvergence behavior of the semi-discrete discontinuous Galerkin (DG) method for scalar nonlinear hyperbolic equations in one spatial dimension. Superconvergence results for problems with fixed and alternating wind ...

In this paper, we develop global superconvergence estimates for the lowest-order Raviart--Thomas mixed finite element method for second-order elliptic equations with general boundary conditions on triangular meshes, where most pairs of adjacent triangles ...

This paper presents a second-order accurate algorithm for calculating an ensemble of solutions to natural convection problems. Solutions are calculated by solving two uncoupled linear systems, each involving a shared coefficient matrix, for multiple ...

We consider a model initial and Dirichlet boundary value problem for a fourth order linear stochastic parabolic equation in one space dimension, forced by an additive space-time white noise. First, we approximate its solution by the solution of an auxiliary ...

In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could be subject to ...

We give a convergence proof for the approximation by sparse collocation of Hilbert-space-valued functions depending on countably many Gaussian random variables. Such functions appear as solutions of elliptic PDEs with lognormal diffusion coefficients. We ...

In this work, we calculate the convergence rate of the finite difference approximation for a class of nonlocal fracture models. We consider two point force interactions characterized by a double well potential. We show the existence of a evolving ...

We develop a family of second-order implicit-explicit (IMEX) schemes for the stiff Bhatnagar--Gross--Krook (BGK) kinetic equation. The method is asymptotic-preserving (can capture the Euler limit without numerically resolving the small Knudsen number) as ...

In this work, we establish a new truncation error estimate of the singular value decomposition (SVD) for a class of Sobolev smooth bivariate functions $ \kappa {\,\in\,} L^2(\Omega,H^s(D))$, $s{\,\geq\,} 0$, and $\kappa\in L^2(\Omega,\dot{H}^s(D))$ with $D ...

Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time step everywhere with a crippling effect on any explicit time-...

The notion of positive realness for linear time-invariant (LTI) dynamical systems, equivalent to passivity, is one of the oldest in system and control theory. In this paper, we consider the problem of finding the nearest positive real (PR) system to a non-...

In this paper we generalize results regarding the order of accuracy of finite difference operators on summation-by-parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a ...

Many applications show that nonconvex nonsmooth regularization has advantages for restoring images with neat edges. This phenomenon has been provided as a mathematical explanation for the anisotropic model through establishing a uniform lower bound for ...

We correct a mistake in the computation of the spatial discretization error in the consistency result in Lemma 5.1 (and the following Theorem 5.2) of the published article [P. Lafitte, A. Lejon, and G. Samaey, SIAM J. Numer. Anal., 54 (2016), pp. 1--33]. ...