相关论文: A robust $C^0$ interior penalty method for a gradi…
In the present study, an interior-exterior penalty discontinuous Galerkin finite element method (DG-FEM) is analysed for solving Elastohydrodynamic lubrication (EHL) line and point contact problems. The existence of discrete penalized…
We propose a new class of nonconvex penalty functions, based on data depth functions, for multitask sparse penalized regression. These penalties quantify the relative position of rows of the coefficient matrix from a fixed distribution…
Constrained optimization with multiple functional inequality constraints has significant applications in machine learning. This paper examines a crucial subset of such problems where both the objective and constraint functions are weakly…
This paper develops an efficient Monte Carlo interior penalty discontinuous Galerkin method for electromagnetic wave propagation in random media. This method is based on a multi-modes expansion of the solution to the time-harmonic random…
Classical interior penalty discontinuous Galerkin (IPDG) methods for diffusion problems require a number of assumptions on the local variation of mesh-size, polynomial degree, and of the diffusion coefficient to determine the values of the,…
The determination of solutions of many inverse problems usually requires a set of measurements which leads to solving systems of ill-posed equations. In this paper we propose the Landweber iteration of Kaczmarz type with general uniformly…
In this paper, we propose an implicit staggered algorithm for crystal plasticity finite element method (CPFEM) which makes use of dynamic relaxation at the constitutive integration level. An uncoupled version of the constitutive system…
This paper presents a novel approach for solving fourth-order phase-field models in brittle fracture mechanics using the Interior Penalty Finite Element Method (IP-FEM). The fourth-order model improves numerical stability and accuracy…
Pointwise divergence free velocity field approximations of the Stokes system are gaining popularity due to their necessity in precise modelling of physical flow phenomena. Several methods have been designed to satisfy this requirement;…
This paper presents a new and efficient numerical algorithm for the biharmonic equation by using weak Galerkin (WG) finite element methods. The WG finite element scheme is based on a variational form of the biharmonic equation that is…
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to relax the divergence constraint of the vector unknown. The…
In general $n$-dimensional simplicial meshes, we propose a family of interior penalty nonconforming finite element methods for $2m$-th order partial differential equations, where $m \geq 0$ and $n \geq 1$. For this family of nonconforming…
We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted…
In this article, goal-oriented a posteriori error estimation for the biharmonic plate bending problem is considered. The error for approximation of goal functional is represented by an estimator which combines dual-weighted residual method…
We investigate a finite element discretization of an elastic bending-plate model with an effective prestrain. The model has been obtained via homogenization and dimension reduction by B\"onlein at al. (2023). Its energy functional is the…
In this paper, we propose an adaptive approach, based on mesh refinement or parametric enrichment with polynomial degree adaption, for numerical solution of convection dominated equations with random input data. A parametric system emerged…
Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the constraints. We first propose an equivalent optimization…
An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that account for an approximation of a folding arc. The numerical…
This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…
In this work, we propose a novel Parameter-Efficient Fine-Tuning (PEFT) approach based on Gaussian Graphical Models (GGMs), marking the first application of GGMs to PEFT tasks, to the best of our knowledge. The proposed method utilizes the…