Related papers: Generalized mixed and primal hybrid methods with a…
We present a stable finite element method for incompressible nonlinear elasticity based on a four-field mixed formulation involving the displacement, displacement gradient, first Piola--Kirchhoff stress and pressure. Unlike existing…
In this article, we design and analyze a Hybrid High-Order (HHO) finite element approximation for a class of strongly nonlinear boundary value problems. We consider an HHO discretization for a suitable linearized problem and show its…
The paper is concerned with a node-based, gradient-driven, continuous adjoint two-phase flow procedure to optimize the shapes of free-floating vessels and discusses three topics. First, we aim to convey that elements of a Cahn-Hilliard…
In this paper, we introduce a \textit{Bi-level OPTimization} (BiOPT) framework for minimizing the sum of two convex functions, where both can be nonsmooth. The BiOPT framework involves two levels of methodologies. At the upper level of…
We propose some finite element schemes to solve a class of fourth-order nonlinear PDEs, which include the vector-valued Landau--Lifshitz--Baryakhtar equation, the Swift--Hohenberg equation, and various Cahn--Hilliard-type equations with…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
In the first part of the paper, we propose and rigorously analyze a mixed finite element method for the approximation of the periodic strong solution to the fully nonlinear second-order Hamilton--Jacobi--Bellman equation with coefficients…
This paper derives some discrete maximum principles for $P1$-conforming finite element approximations for quasi-linear second order elliptic equations. The results are extensions of the classical maximum principles in the theory of partial…
For any complex simple Lie algebra, we generalize primary fileds in the Wess-Zumino-Novikov-Witten conformal field theory with respect to the case of irregular singularities and we construct integral representations of hypergeometric…
In this paper, we propose a robust solver for the finite element discrete problem of the stationary incompressible magnetohydrodynamic (MHD) equations in three dimensions. By the mixed finite element method, both the velocity and the…
We incorporate inertial terms in the hybrid proximal-extragradient algorithm and investigate the convergence properties of the resulting iterative scheme designed for finding the zeros of a maximally monotone operator in real Hilbert…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
We provide both a general framework for discretizing de Rham sequences of differential forms of high regularity, and some examples of finite element spaces that fit in the framework. The general framework is an extension of the previously…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
This work proposes a unified $hp$-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs' type. In particular, we present unified $hp$-HDG…
In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid…
When the obstacle problem of clamped Kirchhoff plates is discretized by a partition of unity method, the resulting discrete variational inequalities can be solved by a primal-dual active set algorithm. In this paper we develop and analyze…
We consider a finite element discretization for the dual Rudin--Osher--Fatemi model using a Raviart--Thomas basis for $H_0 (\mathrm{div};\Omega)$. Since the proposed discretization has splitting property for the energy functional, which is…
This paper presents a proximal bundle (PB) framework based on a generic bundle update scheme for solving the hybrid convex composite optimization (HCCO) problem and establishes a common iteration-complexity bound for any variant belonging…
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…