Related papers: Analysis of A Mixed Finite Element Method for Pois…
The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes…
This paper presents an a priori error analysis of the hp-version of the boundary element method for the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. We use H(div)-conforming discretisations with…
This paper concerns the numerical resolution of a data completion problem for the time-harmonic Maxwell equations in the electric field. The aim is to recover the missing data on the inaccessible part of the boundary of a bounded domain…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
In this paper we show that we can use a modified version of the h-p spectral element method proposed in \cite{duttora1,duttom,duttora2,tomarth} to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal…
We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is…
We consider the singularly perturbed fourth-order boundary value problem $\varepsilon ^{2}\Delta ^{2}u-\Delta u=f $ on the unit square $\Omega \subset \mathbb{R}^2$, with boundary conditions $u = \partial u / \partial n = 0$ on $\partial…
For the finite element solution of Poisson's equation, a local a posteriori error estimation based on the Hypercircle method is proposed. Even for the solution of Poisson's equation without the $H^2$ regularity, this method can provide…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
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…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
We prove several optimal-order error estimates for a finite-element method applied to an inhomogeneous Robin boundary value problem (BVP) for the Poisson equation defined in a smooth bounded domain in $\mathbb{R}^n$, $n=2,3$. The boundary…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
This paper develops a smoothing-based postprocessing method for superconvergence in finite element methods. The method applies a few smoothing iterations, such as damped Jacobi, Gauss-Seidel, or conjugate gradient, with initial guess being…
In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…
We construct a finite element discretization and time-stepping scheme for the incompressible Euler equations with variable density that exactly preserves total mass, total squared density, total energy, and pointwise incompressibility. The…
In this work, a polygonal Reissner-Mindlin plate element is presented. The formulation is based on a scaled boundary finite element method, where in contrast to the original semi-analytical approach, linear shape functions are introduced…
We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…
In this paper the hp-version of the boundary element method is applied to the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. The underlying meshes are supposed to be quasi-uniform. We use…