相关论文: A robust $C^0$ interior penalty method for a gradi…

A posteriori upper and lower bounds are derived for the linear finite element method (FEM) for the Helmholtz equation with large wave number. It is proved rigorously that the standard residual type error estimator seriously underestimates…

We present a systematic study on higher-order penalty techniques for isogeometric mortar methods. In addition to the weak-continuity enforced by a mortar method, normal derivatives across the interface are penalized. The considered…

This paper is concerned with finite element approximations of $W^{2,p}$ strong solutions of second-order linear elliptic partial differential equations (PDEs) in non-divergence form with continuous coefficients. A nonstandard (primal)…

Efficient and accurate numerical algorithms are developed to solve a generalized Kirchhoff-Love plate model subject to three common physical boundary conditions: (i) clamped; (ii) simply supported; and (iii) free. We solve the model…

In this paper, we develop a straightforward $C^0$ linear finite element method for sixth-order elliptic equations. The basic idea is to use gradient recovery techniques to generate higher-order numerical derivatives from a $C^0$ linear…

In this study, we investigate a hybrid-type anisotropic weakly over-penalised symmetric interior penalty method for the Poisson equation on convex domains. Compared with the well-known hybrid discontinuous Galerkin methods, our approach is…

In this paper, we present and analyze an unfitted finite element method for the elliptic interface problem. We consider the case that the interface is $C^2$-smooth or polygonal, and the exact solution $u \in H^{1+s}(\Omega_0 \cup \Omega_1)$…

In this paper, we consider a class of optimization problems constrained to the generalized Stiefel manifold. Such problems are fundamental to a wide range of real-world applications, including generalized canonical correlation analysis,…

This paper presents a reliable and efficient residual-based a posteriori error analysis for the symmetric $H(\operatorname{div}\operatorname{div})$ mixed finite element method for the Kirchhoff-Love plate bending problem with mixed boundary…

We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…

This work focuses on the development of a posteriori error estimates for fourth-order, elliptic, partial differential equations. In particular, we propose a novel algorithm to steer an adaptive simulation in the context of Kirchhoff plates…

We devise and analyze $C^0$-conforming hybrid high-order (HHO) methods to approximate biharmonic problems with either clamped or simply supported boundary conditions. $C^0$-conforming HHO methods hinge on cell unknowns which are…

A preasymptotic error analysis of the finite element method (FEM) and some continuous interior penalty finite element method (CIP-FEM) for Helmholtz equation in two and three dimensions is proposed. $H^1$- and $L^2$- error estimates with…

A new finite element formulation for the Kirchhoff plate model is presented. The method is a displacement formulation with the deflection and the rotation vector as unknowns and it is based on ideas stemming from a stabilized method for the…

We propose a new discontinuous Galerkin (dG) method for a geometrically nonlinear Kirchhoff plate model for large isometric bending deformations. The minimization problem is nonconvex due to the isometry constraint. We present a practical…

An hp-version interior penalty discontinuous Galerkin (IPDG) method under nonconforming meshes is proposed to solve the quad-curl eigenvalue problem. We prove well-posedness of the numerical scheme for the quad-curl equation and then derive…

We employ surface differential calculus to derive models for Kirchhoff plates including in-plane membrane deformations. We also extend our formulation to structures of plates. For solving the resulting set of partial differential equations,…

We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. We derive an hp-reliable and efficient residual type a posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain inverse…

We consider solving the surface Helmholtz equation on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We…

The Kirchhoff plate model plays a vital role in modeling, computing and analyzing the mechanical behaviors of thin plate structures. This study propose a novel fourth-order multi-scale (FOMS) computational method for high-accuracy and…