Numerical Solution for Exterior Problems.
Numerical Solution of a Hyperbolic Free Boundary Problem with a Method of Characteristics.
Numerical solution of a scattering problem in a wave guide using a grid generation technique.
Numerical solution of a three-dimensional integral equation
Numerical solution of parabolic equations in high dimensions
We consider the numerical solution of diffusion problems in for and for in dimension . We use a wavelet based sparse grid space discretization with mesh-width and order , and discontinuous Galerkin time-discretization of order on a geometric sequence of many time steps. The linear systems in each time step are solved iteratively by GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an -error of for where is the total number of operations,...
Numerical solution of parabolic equations in high dimensions
We consider the numerical solution of diffusion problems in (0,T) x Ω for and for T > 0 in dimension dd ≥ 1. We use a wavelet based sparse grid space discretization with mesh-width h and order pd ≥ 1, and hp discontinuous Galerkin time-discretization of order on a geometric sequence of many time steps. The linear systems in each time step are solved iteratively by GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an L2(Ω)-error of O(N-p) for u(x,T)...
Numerical solution of second-order elliptic equations on plane domains
Numerical Solution of Steady-State Porous Flow Free Boundary Problems.
Numerical Solution of the second Boundary value Problem in space
Numerical solutions for second-kind Volterra integral equations by Galerkin methods
In this paper, we study the global convergence for the numerical solutions of nonlinear Volterra integral equations of the second kind by means of Galerkin finite element methods. Global superconvergence properties are discussed by iterated finite element methods and interpolated finite element methods. Local superconvergence and iterative correction schemes are also considered by iterated finite element methods. We improve the corresponding results obtained by collocation methods in the recent...
Numerical Solutions for some Coupled Systems of Nonlinear Boundary Value Problems.
Numerical solutions of cascade flows by finite element method [Abstract of thesis]
Numerical solutions to the Darboux problem with functional dependence.
Numerical studies of groundwater flow problems with a singularity
The paper studies mesh dependent numerical solution of groundwater problems with singularities, caused by boreholes represented as points, instead of a real radius. We show on examples, that the numerical solution of the borehole pumping problem with point source (singularity) can be related to the exact solution of a regular problem with adapted geometry of a finite borehole radius. The radius providing the fit is roughly proportional to the mesh step. Next we define a problem of fracture-rock...
Numerical study of a discrete projection method for rotating incompressible flows.
Numerical study of a new global minimizer for the Mumford-Shah functional in R3
In [Progress Math.233 (2005)], David suggested the existence of a new type of global minimizers for the Mumford-Shah functional in . The singular set of such a new minimizer belongs to a three parameters family of sets . We first derive necessary conditions satisfied by global minimizers of this family. Then we are led to study the first eigenvectors of the Laplace-Beltrami operator with Neumann boundary conditions on subdomains of with three reentrant corners. The necessary conditions are...
Numerical study of natural superconvergence in least-squares finite element methods for elliptic problems
Natural superconvergence of the least-squares finite element method is surveyed for the one- and two-dimensional Poisson equation. For two-dimensional problems, both the families of Lagrange elements and Raviart-Thomas elements have been considered on uniform triangular and rectangular meshes. Numerical experiments reveal that many superconvergence properties of the standard Galerkin method are preserved by the least-squares finite element method.
Numerical study of two sparse AMG-methods
A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.
Numerical Study of Two Sparse AMG-methods
A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.
Numerical treatment of 3-dimensional potential problem
Assuming an incident wave to be a field source, we calculate the field potential in a neighborhood of an inhomogeneous body. This problem which has been formulated in can be reduced to a bounded domain. Namely, a boundary condition for the potential is formulated on a sphere. Then the potential satisfies a well posed boundary value problem in a ball containing the body. A numerical approximation is suggested and its convergence is analyzed.