A numerical solution using an adaptively preconditioned Lanczos method for a class of linear systems related with the fractional Poisson equation.
A Nyström method for boundary integral equations in domains with corners.
A penalty method for topology optimization subject to a pointwise state constraint
This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.
A posteriori error estimates for linear exterior problems via mixed-FEM and DtN mappings
In this paper we combine the dual-mixed finite element method with a Dirichlet-to-Neumann mapping (given in terms of a boundary integral operator) to solve linear exterior transmission problems in the plane. As a model we consider a second order elliptic equation in divergence form coupled with the Laplace equation in the exterior unbounded region. We show that the resulting mixed variational formulation and an associated discrete scheme using Raviart-Thomas spaces are well posed, and derive the...
A posteriori error estimates for the D stabilized Mortar finite element method applied to the Laplace equation
We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also estimates...
A posteriori Error Estimates For the 3D Stabilized Mortar Finite Element Method applied to the Laplace Equation
We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also estimates...
A priori error analysis of a fully-mixed finite element method for a two-dimensional fluid-solid interaction problem
We introduce and analyze a fully-mixed finite element method for a fluid-solid interaction problem in 2D. The model consists of an elastic body which is subject to a given incident wave that travels in the fluid surrounding it. Actually, the fluid is supposed to occupy an annular region, and hence a Robin boundary condition imitating the behavior of the scattered field at infinity is imposed on its exterior boundary, which is located far from the obstacle. The media are governed by the elastodynamic...
A priori estimates in weighted spaces for solutions of the Poisson and heat equations
We prove a priori estimates for solutions of the Poisson and heat equations in weighted spaces of Kondrat'ev type. The weight is a power of the distance from a distinguished axis.
A Property of Biharmonic Functions with Dirichlet Finite Laplacians.
A Quantitative Discrete H2-Regularity Estimate for the Shortley-Weller Scheme in Convex Domains.
A regularity result for boundary value problems on Lipschitz domains
A regularized Newton method in electrical impedance tomography using shape Hessian information
A remark on the blowup of solutions to the Laplace equations with nonlinear dynamical boundary conditions.
A remark on two dimensional periodic potentials.
A Right-Inverse for the Divergence Operator in Spaces of Piecewise Polynomials. Application to the p-Version of the Finite Element Method
A shape optimization approach for a class of free boundary problems of Bernoulli type
We are interested in an optimal shape design formulation for a class of free boundary problems of Bernoulli type. We show the existence of the optimal solution of this problem by proving continuity of the solution of the state problem with respect to the domain. The main tools in establishing such a continuity are a result concerning uniform continuity of the trace operator with respect to the domain and a recent result on the uniform Poincaré inequality for variable domains.
A special finite element method based on component mode synthesis
The goal of our paper is to introduce basis functions for the finite element discretization of a second order linear elliptic operator with rough or highly oscillating coefficients. The proposed basis functions are inspired by the classic idea of component mode synthesis and exploit an orthogonal decomposition of the trial subspace to minimize the energy. Numerical experiments illustrate the effectiveness of the proposed basis functions.
A splitting formula for an electromagnetic diffraction problem.
A Stationary Schrödinger-Poisson System Arising from the Modelling of Electronic Devices.
A symmetry problem
Consider the Newtonian potential of a homogeneous bounded body D ⊂ ℝ³ with known constant density and connected complement. If this potential equals c/|x| in a neighborhood of infinity, where c>0 is a constant, then the body is a ball. This known result is now proved by a different simple method. The method can be applied to other problems.