Related papers: Error estimates for variational normal derivatives…
We study stochastic Navier-Stokes equations in two dimensions with respect to periodic boundary conditions. The equations are perturbed by a nonlinear multiplicative stochastic forcing with linear growth (in the velocity) driven by a…
Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the…
We study the Dirichlet problem for the weighted Schr\"odinger operator \[-\Delta u +Vu = \lambda \rho u,\] where $\rho$ is a positive weighting function and $V$ is a potential. Such equations appear naturally in conformal geometry and in…
This work presents error analysis for a finite element method applied to a two-dimensional singularly perturbed convection-diffusion turning point problem. Utilizing a layer-adapted Shishkin mesh, we prove uniform convergence in the maximum…
In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. In particular, we consider the strong form of the equation using standard graph Laplacian matrices and also weak forms…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
We prove non-asymptotic rates of convergence in the $W^{s,2}(\mathbb R^d)$-norm for the solution of the fractional Dirichlet problem to the solution of the local Dirichlet problem as $s\uparrow 1$. For regular enough boundary values we get…
We estimate the error of the Deep Ritz Method for linear elliptic equations. For Dirichlet boundary conditions, we estimate the error when the boundary values are imposed through the boundary penalty method. Our results apply to arbitrary…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide…
This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…
This paper analyses the finite element component of the error when using preintegration to approximate the cdf and pdf for uncertainty quantification (UQ) problems involving elliptic PDEs with random inputs. It is a follow up to Gilbert,…
In this paper, we examine a finite element approximation of the steady $p(\cdot)$-Navier-Stokes equations ($p(\cdot)$ is variable dependent) and prove orders of convergence by assuming natural fractional regularity assumptions on the…
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…
We present a posteriori error estimates for finite element approximations in a minimization approach to a coefficient inverse problem. The problem is that of reconstructing the dielectric permittivity $\varepsilon =…
We consider a mixed finite element method for a biharmonic equation with clamped boundary conditions based on biorthogonal systems with weakly imposed Dirichlet boundary condition. We show that the weak imposition of the boundary condition…
In this paper, we consider elliptic boundary value problems with discontinuous coefficients and obtain the asymptotic optimal error estimate $\|u-u_k\|_{1,\Omega}\leqslant Ch|\ln h|^{1/2}\|u\|_{2,\Omega_1+\Omega_2}$ for triangle linear…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion-convection-reaction equations and boundary conditions of mixed type. Since neither conformity…
We present useful connections between the finite difference and the finite element methods for a model boundary value problem. We start from the observation that, in the finite element context, the interpolant of the solution in one…