A regularity result for boundary value problems on Lipschitz domains
A regularity theorem for linear second order elliptic divergence equations
A Relaxation Procedure for Domain Decomposition Methods Using Finite Elements.
A remark on the blowup of solutions to the Laplace equations with nonlinear dynamical boundary conditions.
A remark on the existence of large solutions via sub and supersolutions.
A Remark on the L... Bounds of the Ritz Operator Associated with a Finite Element Approximation.
A robust and parallel multigrid method for convection diffusion equations.
A second eigenvalue bound for the Dirichlet-Schrödinger equation with a radially symmetric potential.
A second-order finite volume element method on quadrilateral meshes for elliptic equations
In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in -norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the method.
A second-order finite volume element method on quadrilateral meshes for elliptic equations
In this paper, by use of affine biquadratic elements, we construct and analyze a finite volume element scheme for elliptic equations on quadrilateral meshes. The scheme is shown to be of second-order in H1-norm, provided that each quadrilateral in partition is almost a parallelogram. Numerical experiments are presented to confirm the usefulness and efficiency of the 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 sharp result on the poles localization for a Gevrey convex body
In this talk we extend to Gevrey-s obstacles with a result on the poles free zone due to J. Sjöstrand [8] for the analytic case.
A sign-changing solution for a superlinear Dirichlet problem. II.
A solution method of the Signorini problem.
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 stable mixed finite element method on truncated exterior domains
A stable multigrid strategy for convection-diffusion using high order compact discretization.
A Static condensation Reduced Basis Element method : approximation and a posteriori error estimation
We propose a new reduced basis element-cum-component mode synthesis approach for parametrized elliptic coercive partial differential equations. In the Offline stage we construct a Library of interoperable parametrized reference components relevant to some family of problems; in the Online stage we instantiate and connect reference components (at ports) to rapidly form and query parametric systems. The method is based on static condensation at the interdomain level, a conforming eigenfunction “port”...
A stationary Stefan problem with convection and nonlinear diffusion.
A strongly degenerate quasilinear equation : the elliptic case
We prove existence and uniqueness of entropy solutions for the Neumann problem for the quasilinear elliptic equation , where , , and is a convex function of with linear growth as , satisfying other additional assumptions. In particular, this class includes the case where , , being a convex function with linear growth as . In the second part of this work, using Crandall-Ligget’s iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions for the...