Related papers: A Two-Stage Finite Element Approach for High-preci…
The presented article contains a 2D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes with a prescribed size h of elements. These finite element meshes can serve as standard discrete…
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…
In nodal based finite element method (FEM), degrees of freedom are associated with the nodes of the element whereas, for edge FEM, degrees of freedom are assigned to the edges of the element. Edge element is constructed based on Whitney…
This paper is dedicated to the rigorous numerical analysis of a Multiscale Finite Element Method (MsFEM) for the Stokes system, when dealing with highly heterogeneous media, as proposed in [B.P.~Muljadi et al., arXiv:1404.2837]. The method…
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…
Finite-sum optimization plays an important role in the area of machine learning, and hence has triggered a surge of interest in recent years. To address this optimization problem, various randomized incremental gradient methods have been…
We design and analyze an adaptive $hp$-finite element method (hp-AFEM) in dimensions $n=1,2$. The algorithm consists of iterating two routines: hp-NEARBEST finds a near-best $hp$-approximation of the current discrete solution and data to a…
This paper is devoted to analyze of nonconforming finite volume methods (FVMs), whose trial spaces are chosen as the nonconforming finite element (FE) spaces, for solving the second order elliptic boundary value problems. We formulate the…
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).…
This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods…
In this paper, we observe an interesting phenomenon for a hybridizable discontinuous Galerkin (HDG) method for eigenvalue problems. Specifically, using the same finite element method, we may achieve both upper and lower eigenvalue bounds…
This paper presents high-order numerical methods for solving boundary value problems associated with the Lane-Emden equation, which frequently arises in astrophysics and various nonlinear models. A major challenge in studying this equation…
We propose in this paper a multilevel correction method to solve optimal control problems constrained by elliptic equations with the finite element method. In this scheme, solving optimization problem on the finest finite element space is…
Robust parameter estimation is a crucial task in several 3D computer vision pipelines such as Structure from Motion (SfM). State-of-the-art algorithms for robust estimation, however, still suffer from difficulties in converging to…
We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types of…
This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an…
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…
We present a high-precision solution of Dirac equation by numerically solving the minmax two-center Dirac equation with the finite element method (FEM). The minmax FEM provide a highly accurate benchmark result for systems with light or…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…