Related papers: An efficient mixed finite element method for nonli…
We review some recent advances in the field of element-based algebraic stabilization for continuous finite element discretizations of nonlinear hyperbolic problems. The main focus is on multidimensional convex limiting techniques designed…
Maxwell's equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of…
We design and analyze an iterative two-grid algorithm for the finite element discretizations of strongly nonlinear elliptic boundary value problems in this paper. We propose an iterative two-grid algorithm, in which a nonlinear problem is…
In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematic hardening is analyzed. Thereby, the non-differentiability of the involved plasticity functional is resolved by a Lagrange multiplier leading…
The Landau--Lifshitz--Baryakhtar (LLBar) and the Landau--Lifshitz--Bloch (LLBloch) equations are nonlinear vector-valued PDEs which arise in the theory of micromagnetics to describe the dynamics of magnetic spin field in a ferromagnet at…
We shall propose and analyze some new preconditioners for the saddle-point systems arising from the edge element discretization of the time-harmonic Maxwell equations in three dimensions. We will first consider the saddle-point systems with…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…
In this article we investigate a finite element formulation of strongly monotone quasi-linear elliptic PDEs in the context of fixed-point iterations. As opposed to Newton's method, which requires information from the previous iteration in…
Geometric particle-in-cell discretizations have been derived based on a discretization of the fields that is conforming with the de Rham structure of the Maxwell's equation and a standard particle-in-cell ansatz for the fields by deriving…
We propose and analyze two convection quasi-robust and pressure robust finite element methods for a fully nonlinear time-dependent magnetohydrodynamics problem. Both methods employ the $H_{\rm div}$ conforming BDM element coupled with an…
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
In this paper, we propose a unified framework, the Hessian discretisation method (HDM), which is based on four discrete elements (called altogether a Hessian discretisation) and a few intrinsic indicators of accuracy, independent of the…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…
This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjoint state are related through the control on the boundary of…