相关论文: Optimal multilevel adaptive FEM for the Argyris el…

In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…

A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…

The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…

This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower…

We consider adaptive finite element methods (AFEMs) with inexact algebraic solvers for second-order symmetric linear elliptic diffusion problems. Optimal complexity of AFEM, i.e., optimal convergence rates with respect to the overall…

We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…

We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…

The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps…

This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…

We develop all of the components needed to construct an adaptive finite element code that can be used to approximate fractional partial differential equations, on non-trivial domains in $d\geq 1$ dimensions. Our main approach consists of…

We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…

We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…

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…

In this paper, we present several new a posteriori error estimators and two adaptive mixed finite element methods \textsf{AMFEM1} and \textsf{AMFEM2} for the Hodge Laplacian problem in finite element exterior calculus. We prove that…

Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are…

A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such…

Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

This paper addresses the efficient solution of linear systems arising from curl-conforming finite element discretizations of $H(\mathrm{curl})$ elliptic problems with heterogeneous coefficients. We first employ the discrete form of a…