A Boundary Element Method for a Two-Dimensional Interface Problem in Electromagnetics.
A Discrete Sampling Inversion Scheme for the Heat Equation.
A Galerkin spectral approximation in linearized beam theory
A Legendre spectral collocation method for the biharmonic Dirichlet problem
A Legendre Spectral Collocation Method for the Biharmonic Dirichlet Problem
A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplacian of the solution on the two vertical sides of the square. The Schur complement system is solved by a...
A new formulation of the Stokes problem in a cylinder, and its spectral discretization
We analyze a new formulation of the Stokes equations in three-dimensional axisymmetric geometries, relying on Fourier expansion with respect to the angular variable: the problem for each Fourier coefficient is two-dimensional and has six scalar unknowns, corresponding to the vector potential and the vorticity. A spectral discretization is built on this formulation, which leads to an exactly divergence-free discrete velocity. We prove optimal error estimates.
A new formulation of the Stokes problem in a cylinder, and its spectral discretization
We analyze a new formulation of the Stokes equations in three-dimensional axisymmetric geometries, relying on Fourier expansion with respect to the angular variable: the problem for each Fourier coefficient is two-dimensional and has six scalar unknowns, corresponding to the vector potential and the vorticity. A spectral discretization is built on this formulation, which leads to an exactly divergence-free discrete velocity. We prove optimal error estimates.
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 Quadrature-Based Approach to Improving the Collocation Method.
A reduced basis element method for the steady Stokes problem
The reduced basis element method is a new approach for approximating the solution of problems described by partial differential equations. The method takes its roots in domain decomposition methods and reduced basis discretizations. The basic idea is to first decompose the computational domain into a series of subdomains that are deformations of a few reference domains (or generic computational parts). Associated with each reference domain are precomputed solutions corresponding to the same...
A remark to the finite element method
A spectral-Tau approximation for the Stokes and Navier-Stokes equations
About biharmonic problem via a spectral approach and decomposition techniques.
Adaptive Boundary Element Methods for Strongly Elliptic Integral Equations.
Algorithm 48. Solving boundary value problems for the biharmonic equation by the method of summary representations
An accurate solution of the Poisson equation by the Legendre tau method.
An alternating direction implicit method for orthogonal spline collocation linear systems.
An Iteration Scheme for Boundary Value-Alternative Problems.
Approximate solution of the one-dimensional heat conduction equation by the boundary element method
Approximation of Burgers' equation by pseudo-spectral methods