数值分析
This work investigates a fully discrete mixed finite element method for the stochastic Boussinesq system driven by multiplicative noise. The spatial discretization is performed using a standard mixed finite element method, while the…
This work investigates inexact block Schur complement preconditioning for linear poroelasticity problems discretized using a hybrid approach: Bernardi-Raugel elements for solid displacement and lowest-order weak Galerkin elements for fluid…
This paper presents a streamfunction-vorticity formulation for the Navier--Stokes and Euler equations on general surfaces. Notably, this includes non-simply connected surfaces, on which the harmonic components of the velocity field play a…
This paper is devoted to the theoretical study of the efficiency, namely, stability of some greedy algorithms. In the greedy approximation theory researchers are mostly interested in the following two important properties of an algorithm --…
Certain energy-conservative Galerkin discretizations for nonlinear dispersive wave equations have revealed an unusual convergence behavior: optimal convergence is attained when continuous Lagrange finite element spaces of odd polynomial…
We investigate non-overlapping Schwarz preconditioners for the algebraic systems stemming from high-order discretizations of the coupled monodomain and Barreto-Cressman models, with applications to brain electrophysiology. The spatial…
Explicit details are presented for calculation of $A^+B$, $A^+AB$ and $AA^+B$ where $A_{m\times n}$ is any nonzero matrix, $A^+$ is the Moore-Penrose pseudoinverse of $A$ and $B$ is any matrix of appropriate dimensions, where the quantities…
We present the Fast Newton Transform (FNT), an algorithm for performing $m$-variate Newton interpolation in downward closed polynomial spaces with time complexity $\mathcal{O}(|A|m\overline{n})$. Here, $A$ is a downward closed set of…
Solving high-dimensional partial differential equations (PDEs) is a critical challenge where modern data-driven solvers often lack reliability and rigorous error guarantees. We introduce Simulation-Calibrated Scientific Machine Learning…
The article is devoted to the construction of examples that illustrate (using computer calculations) the rate of convergence of Chernoff approximations to the solution of the Cauchy problem for the heat equation. We are interested in the…
This paper studies the approximation capacity of neural networks with an arbitrary activation function and with norm constraint on the weights. Upper and lower bounds on the approximation error of these networks are computed for smooth…
We propose a second-order implicit-explicit (IMEX) time-stepping scheme for the isentropic, compressible Cahn-Hilliard-Navier-Stokes equations discretized on staggered (MAC) grids. The scheme is based on finite difference approximations…
The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
This work proposes a novel approach for designing high-order energy-decaying schemes for Maxwell's equations in Havriliak-Negami dispersive media. It is shown that conventional convolution quadrature (CQ) methods, which rely directly on the…
We propose the Manifold Function Encoder (MFE) for identifying different functions defined on different manifolds. Both a manifold in Euclidean space and a function defined on this manifold can be viewed as bounded linear functionals on a…
Defeaturing, the process of simplifying computational geometries, is a critical step in industrial simulation pipelines for reducing computational cost. Rigorous a posteriori estimators exist for the global energy-norm error introduced by…
We develop an enriched Galerkin (EG) method for the incompressible Navier-Stokes equations that conserves both kinetic energy and helicity in the inviscid limit without introducing any additional projection variables. The method employs an…
We propose and study a general quasi-interpolation framework for stochastic function approximation, which stems and draws motivation from convolution-type solutions for certain practical weighted variational problems. We obtain our…
We consider a Lattice Boltzmann type discrete velocity model in the low Mach number scaling and develop a corresponding numerical scheme that remains uniformly valid across all regimes of the mean free path, from the kinetic to the…