Related papers: A Multilevel Correction Scheme for Nonsymmetric Ei…
In this paper, we study the numerical method for the bi-Laplace problems with inhomogeneous coefficients; particularly, we propose finite element schemes on rectangular grids respectively for an inhomogeneous fourth-order elliptic singular…
We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…
We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the…
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…
In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domains and triple-junction points. We construct new IFE functions on elements intersected with…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
In this paper we prove the optimal convergence of a standard adaptive scheme based on edge finite elements for the approximation of the solutions of the eigenvalue problem associated with Maxwell's equations. The proof uses the known…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche's method. Since the non-matching meshes can result in arbitrarily…
We propose a multi-index algorithm for the Monte Carlo (MC) discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows a multi-level finite-element approximation in the physical…
In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…
This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on $\ell_2$, the space of square summable…
This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated…
This study proposes a class of augmented subspace schemes for the weak Galerkin (WG) finite element method used to solve eigenvalue problems. The augmented subspace is built with the conforming linear finite element space defined on the…
In this paper, we examine the effectiveness of classic multiscale finite element method (MsFEM) (Hou and Wu, 1997; Hou et al., 1999) for mixed Dirichlet-Neumann, Robin and hemivariational inequality boundary problems. Constructing so-called…
The paper develops an explicit a priori error estimate for finite element solution to nonhomogeneous Neumann problems. For this purpose, the hypercircle equation over finite element spaces is constructed and the explicit upper bound of the…
In this paper, we first establish the convergence criteria of the residual iteration method for solving quadratic eigenvalue problem- s. We analyze the impact of shift point and the subspace expansion on the convergence of this method. In…
We introduce the Morse parametric qualification condition for bilevel programming. Generic semi-algebraic functions are Morse parametric in a piecewise sense. Thus, bilevel programs with a Morse parametric lower level constitute a relevant…