Related papers: Finite Element Error Estimates on Geometrically Pe…
We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…
We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical…
We present a numerical analysis of a higher order unfitted space-time Finite Element method applied to a convection-diffusion model problem posed on a moving bulk domain. The method uses isoparametric space-time mappings for the geometry…
We derive explicit a priori consistency error estimates for a standard finite element discretization of the Poisson equation on convex domains, where the domain is approximated by an internal convex polyhedron. The obtained explicit…
In this paper we provide some error estimates for the div least-squares finite element method on elliptic problems. The main contribution is presenting a complete error analysis, which improves the current \emph{state-of-the-art} results.…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
In this paper we propose a finite element method for solving elliptic equations with the observational Dirichlet boundary data which may subject to random noises. The method is based on the weak formulation of Lagrangian multiplier. We show…
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…
This paper addresses the estimation of uncertain distributed diffusion coefficients in elliptic systems based on noisy measurements of the model output. We formulate the parameter identification problem as an infinite dimensional…
Elliptic partial differential equations on surfaces play an essential role in geometry, relativity theory, phase transitions, materials science, image processing, and other applications. They are typically governed by the Laplace-Beltrami…
We consider a sketched implementation of the finite element method for elliptic partial differential equations on high-dimensional models. Motivated by applications in real-time simulation and prediction we propose an algorithm that…
Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman equations in the context of stochastic optimal control, or…
We propose an analysis for the stabilized finite element methods proposed in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations. SIAM J. Sci. Comput., 35(6) 2013,…
In this paper, we consider the numerical approximation of time-fractional parabolic problems involving Caputo derivatives in time of order $\alpha$, $0< \alpha<1$. We derive optimal error estimates for semidiscrete Galerkin FE type…
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove convergence of an…
We study a discretization technique for the parabolic fractional obstacle problem in bounded domains. The fractional Laplacian is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation posed on a semi-infinite…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and $L^2$ norms of the error. Using stabilization terms we show that the resulting algebraic…
In this article, we analyse the domain mapping method approach to approximate statistical moments of solutions to linear elliptic partial differential equations posed over random geometries including smooth surfaces and bulk-surface…
We consider the Weak Galerkin finite element approximation of the Singularly Perturbed Biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution…