A note on very weak -harmonic mappings.
A note on weighted estimates for the Schrödinger operator.
A numerical approach to a class of unilateral elliptic problems of non-variational type
A numerical minimization scheme for the complex Helmholtz equation
We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method and illustrate...
A numerical minimization scheme for the complex Helmholtz equation
We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method and illustrate...
A numerical solution using an adaptively preconditioned Lanczos method for a class of linear systems related with the fractional Poisson equation.
A numerical study on Neumann-Neumann methods for hp approximations on geometrically refined boundary layer meshes II. Three-dimensional problems
In this paper, we present extensive numerical tests showing the performance and robustness of a Balancing Neumann-Neumann method for the solution of algebraic linear systems arising from hp finite element approximations of scalar elliptic problems on geometrically refined boundary layer meshes in three dimensions. The numerical results are in good agreement with the theoretical bound for the condition number of the preconditioned operator derived in [Toselli and Vasseur, IMA J. Numer. Anal.24 (2004)...
A numerically based investigation on the symmetry breaking and asymptotic behavior of the ground states to the -Hénon equation.
A Nyström method for boundary integral equations in domains with corners.
A one-dimensional nonlinear degenerate elliptic equation.
A -Laplacian system with resonance and nonlinear boundary conditions on an unbounded domain
We study a nonlinear elliptic system with resonance part and nonlinear boundary conditions on an unbounded domain. Our approach is variational and is based on the well known Landesman-Laser type conditions.
A parallel AMG for overlapping and non-overlapping domain decomposition.
A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods.
A parallel multigrid method using the full domain partition.
A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations
A parameter-free stabilized finite element method for scalar advection-diffusion problems
We formulate and study numerically a new, parameter-free stabilized finite element method for advection-diffusion problems. Using properties of compatible finite element spaces we establish connection between nodal diffusive fluxes and one-dimensional diffusion equations on the edges of the mesh. To define the stabilized method we extend this relationship to the advection-diffusion case by solving simplified one-dimensional versions of the governing equations on the edges. Then we use H(curl)-conforming...
A partial regularity result for a class of stationary Yang-Mills in high dimension.
We prove, for arbitrary dimension of the base n greater than or equal to 4, stationary Yang-Mills Fields satisfying Borne approximability property are regular apart from a closed subset of the base having zero (n-4)- Hausdorff measure.
A Partial Solution of the Pompeiu Problem.
A pattern formation problem on the sphere.
A penalty method for approximations of the stationary power-law Stokes problem.