Related papers: Finite element error estimates for normal derivati…
This paper is concerned with the homogenization of Dirichlet problem of elliptic systems in a bounded, smooth domain of finite type. Both the coefficients of the elliptic operator and the Dirichlet boundary data are assumed to be periodic…
We prove quasi-optimal $L^\infty$ norm error estimates (up to logarithmic factors) for the solution of Poisson's problem by the standard Hybridizable Discontinuous Galerkin (HDG) method. Although such estimates are available for conforming…
We study the elliptic equation with a line Dirac delta function as the source term subject to the Dirichlet boundary condition in a two-dimensional domain. Such a line Dirac measure causes different types of solution singularities in the…
In this article, we aim to recover locally conservative and $H(div)$ conforming fluxes for the linear Cut Finite Element Solution with Nitsche's method for Poisson problems with Dirichlet boundary condition. The computation of the…
This paper is concerned with finite element methods for Poisson's equation with rough boundary data. Conventional methods require that the boundary data $g$ of the problem belongs to $H^{1/2} (\partial \Omega)$. However, in many…
In this paper we prove convergence results for homogenization problem for solutions of partial differential system with rapidly oscillating Dirichlet data. Our method is based on analysis of oscillatory integrals. In the uniformly convex…
In this paper, we investigate boundary estimates for the Dirichlet problem for a class of fully nonlinear elliptic equations with general boundary conditions, including nonzero boundary conditions. Given specific structural conditions on…
Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…
We consider an initial- and Dirichlet boundary- value problem for a fourth-order linear stochastic parabolic equation, in two or three space dimensions, forced by an additive space-time white noise. Discretizing the space-time white noise a…
In recent work, Li et al.\ (Comm.\ Math.\ Sci., 7:81-107, 2009) developed a diffuse-domain method (DDM) for solving partial differential equations in complex, dynamic geometries with Dirichlet, Neumann, and Robin boundary conditions. The…
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,…
In this paper, we present a nonlocal model for Poisson equation and corresponding eigenproblem with Dirichlet boundary condition. In the direct derivation of the nonlocal model, normal derivative is required which is not known for Dirichlet…
We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estimates are optimal in dimensions larger than three and new in…
In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee. The cut finite element method is a fictitious domain method with Nitsche type…
In this paper, we investigate a sixth order elliptic equation with the simply supported boundary conditions in a polygonal domain. We propose a new method that decouples the sixth order problem into a system of second order equations.…
There are many application papers that solve elliptic boundary value problems by meshless methods, and they use various forms of generalized stiffness matrices that approximate derivatives of functions from values at scattered nodes…
We prove a convergence result for a natural discretization of the Dirichlet problem of the elliptic Monge-Ampere equation using finite dimensional spaces of piecewise polynomial C0 or C1 functions. Standard discretizations of the type…
We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of [Carstensen et al., Comput. Math. Appl. 67 (2014)]. We prove that this framework covers standard…
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The PDE is discretized via a multi-domain spectral collocation method of high local order (order 30 and…