Related papers: Stabilised finite element methods for ill-posed pr…
We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…
We present a stable and convergent mixed finite element method (MFEM) for the linear regularized 13-moment (R13) equations in rarefied gas dynamics. Unlike existing methods that require stabilization via penalty terms, our scheme achieves…
A stabilized finite element method is introduced for the simulation of time-periodic creeping flows, such as those found in the cardiorespiratory systems. The new technique, which is formulated in the frequency rather than time domain,…
In this work, we propose a bi-grid scheme framework for the Allen-Cahn equation in Finite Element Method. The new methods are based on the use of two FEM spaces, a coarse one and a fine one, and on a decomposition of the solution into mean…
This work presents a new conforming stabilized virtual element method for the generalized Boussinesq equation with temperature-dependent viscosity and thermal conductivity. A gradient-based local projection stabilization method is…
In this work, we extend the equal-order stabilized scheme discussed in [Franca et al., Comput. Methods Appl. Mech. Engrg. 99 (1992) 209-233] to accommodate slip (i.e., Navier) boundary conditions for the stationary Navier-Stokes equations.…
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…
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on a monolithic convex limiting approach and prove a…
In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive…
In this paper, we investigate the combination of a linear continuous interior penalty type and a non-linear artificial diffusion stabilisation applied to the transport problem, based on continuous Galerkin finite elements in space. This…
In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results…
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…
This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for finite-time stability are presented via state…
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…
In this work we address the analysis of the stationary generalized Burgers-Huxley equation (a nonlinear elliptic problem with anomalous advection) and propose conforming, nonconforming and discontinuous Galerkin finite element methods for…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
We analyse the Virtual Element Methods (VEM) on a simple elliptic model problem, allowing for more general meshes than the one typically considered in the VEM literature. For instance, meshes with arbitrarily small edges (with respect to…
We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on…
In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…
In this paper, we formulate, analyse and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche's technique for virtual element methods. The divergence…