相关论文: Approximation of single layer distributions by Dir…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson…
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…
This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions. Using the matrix transform method the fractional Laplacian operator…
A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…
We consider standard tracking-type, distributed elliptic optimal control problems with $L^2$ regularization, and their finite element discretization. We are investigating the $L^2$ error between the finite element approximation $u_{\varrho…
The purpose of this work is to introduce and analyze a numerical scheme to efficiently solve boundary value problems involving the spectral fractional Laplacian. The approach is based on a reformulation of the problem posed on a…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
We develop and analyse finite volume methods for the Poisson problem with boundary conditions involving oblique derivatives. We design a generic framework, for finite volume discretisations of such models, in which internal fluxes are not…
A common approach is present concerning the problem of Dirichlet, both for bounded 3D domains and their (unbounded) complements, regarding the fractional (3D) Poisson equation.
A method is described to solve the Poisson problem for a three dimensional source distribution that is periodic into one direction. Perpendicular to the direction of periodicity a free space (or open) boundary is realized. In beam physics,…
Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most straightforwardly by a diffusion equation with suitable flux…
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…
This paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems, and…
We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result. Based upon this we provide a numerical analysis of high…
Several physical problems modeled by second-order elliptic equations can be efficiently solved using mixed finite elements of the Raviart-Thomas family RTk for N-simplexes, introduced in the seventies. In case Neumann conditions are…
In this article, we derive the asymptotic expansion, up to an arbitrary order in theory, for the solution of a two-dimensional elliptic equation with strongly anisotropic diffusion coefficients along different directions, subject to the…
In this paper we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
This work is motivated by the need to develop efficient tools for uncertainty quantification in subsurface flows associated with radioactive waste disposal studies. We consider single phase flow problems in random porous media described by…