SIAM Journal on Numerical Analysis

This paper introduces and analyzes the combined use of the virtual element method (VEM) and the boundary element method (BEM) to numerically solve linear transmission problems in two and three dimensions. As a model, we consider an elliptic equation in ...

We present a method for the fast computation of the eigenpairs of a bijective positive symmetric linear operator $\mathcal{L}$. The method is based on a combination of operator adapted wavelets (gamblets) with hierarchical subspace correction. First, ...

In this paper, we first devise an ensemble hybridizable discontinuous Galerkin (HDG) method to efficiently simulate a group of parameterized convection diffusion PDEs. These PDEs have different coefficients, initial conditions, source terms, and boundary ...

In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schrödinger equation for molecules in the Born--Oppenheimer approximation. In this article, we analyze the tailored coupled-cluster ...

We address the numerical computation of distance maps with respect to Riemannian metrics of strong anisotropy. For that purpose we solve generalized eikonal equations, discretized using adaptive upwind finite differences on a Cartesian grid, in a single ...

We consider a class of nonlinear saddle point problems with various applications in PDEs and optimal control problems and propose an algorithmic framework based on some inexact Uzawa methods in the literature. Under mild conditions, the convergence of ...

This paper considers a hyperbolic Maxwell variational inequality with temperature effects arising from Bean's critical-state model in type-II (high-temperature) superconductivity. Here, temperature dependence is included in the critical current density ...

The value of a highly oscillatory integral is typically determined asymptotically by the behavior of the integrand near a small number of critical points. These include the endpoints of the integration domain and the so-called stationary points or saddle ...

We present the divergence-free nonconforming virtual element method for the Stokes problems. We first construct a nonconforming virtual element with continuous normal component and weak continuous tangential component by enriching the previous $\bm H$(div)...

A modified weighted essentially nonoscillatory (WENO) reconstruction technique preventing accuracy loss near critical points (regardless of their order) of the underlying data is presented. This approach only uses local data from the reconstruction ...

We consider primal dual mixed finite element methods for the advection-diffusion equation. For the primal variable we use standard continuous finite element space and for the flux we use the Raviart-Thomas space. We prove optimal a priori error estimates in ...

In this article we consider the smoothing problem for hidden Markov models. Given a hidden Markov chain $\{X_n\}_{n\geq 0}$ and observations $\{Y_n\}_{n\geq 0}$, our objective is to compute $\mathbb{E}[\varphi(X_0,\dots,X_k)|y_{0},\dots,y_n]$ for some real-...

In this paper, we present a fast $(3-\alpha)$-order numerical method for the Caputo fractional derivative based on the L2 scheme and the sum-of-exponentials (SOE) approximation to the convolution kernel involved in the fractional derivative. This work can be ...

We further develop a simple modification of Runge--Kutta methods that guarantees conservation or stability with respect to any inner-product norm. The modified methods can be explicit and retain the accuracy and stability properties of the unmodified Runge--...