相关论文: On $p$-robust saturation on quadrangulations

We consider the problem of robust polynomial regression, where one receives samples $(x_i, y_i)$ that are usually within $\sigma$ of a polynomial $y = p(x)$, but have a $\rho$ chance of being arbitrary adversarial outliers. Previously, it…

An expandable local and parallel two-grid finite element scheme based on superposition principle for elliptic problems is proposed and analyzed in this paper by taking example of Poisson equation. Compared with the usual local and parallel…

In this paper we show that we can use a modified version of the h-p spectral element method proposed in \cite{duttora1,duttom,duttora2,tomarth} to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal…

We study a local thinning $T_r$ that retains a point with probability $p(n_r)$, where $n_r$ counts neighbors within radius $r$. For Poisson input with spatially varying intensity, we obtain an exact intensity via a Poisson--mixture formula…

The main aim of this paper is to document the performance of $p$-refinement with respect to maximum principles and the non-negative constraint. The model problem is (steady-state) anisotropic diffusion with decay (which is a second-order…

In this work, we exploit the capability of virtual element methods in accommodating approximation spaces featuring high-order continuity to numerically approximate differential problems of the form $\Delta^p u =f$, $p\ge1$. More…

We consider stopping criteria that balance algebraic and discretization errors for the conjugate gradient algorithm applied to high-order finite element discretizations of Poisson problems. Firstly, we introduce a new stopping criterion…

We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson…

Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…

This paper considers the finite element solution of the boundary value problem of Poisson's equation and proposes a guaranteed em a posteriori local error estimation based on the hypercircle method. Compared to the existing literature on…

The first part of the cumulative thesis contains the numerical analysis of different $hp$-finite element discretizations related to two different weak formulations of a model problem in elastoplasticity with linearly kinematic hardening.…

We consider an adaptive finite element method with arbitrary but fixed polynomial degree $p \ge 1$, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [Diening et al, Found.…

We discuss the $p$- and the $hp$-versions of the virtual element method for the approximation of eigenpairs of elliptic operators with a potential term on polygonal meshes. An application of this model is provided by the Schr\"odinger…

We present a local construction of H(curl)-conforming piecewise polynomials satisfying a prescribed curl constraint. We start from a piecewise polynomial not contained in the H(curl) space but satisfying a suitable orthogonality property.…

In this paper we are concerned with convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain exhibiting highly oscillatory behavior in part of its boundary. We deal with the resonant…

We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…

In this work we present an adaptive Newton-type method to solve nonlinear constrained optimization problems in which the constraint is a system of partial differential equations discretized by the finite element method. The adaptive…

The purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P1 polynomials for every variable (velocity, pressure and…

We rigorously derive a homogenized model for the Poisson--Nernst--Planck (PNP) equations for the case of multiple species defined on a periodic porous medium in spatial dimensions two and three. This extends the previous homogenization…

Optimization methods that make use of derivatives of the objective function up to order $p > 2$ are called tensor methods. Among them, ones that minimize a regularized $p$th-order Taylor expansion at each step have been shown to possess…