The beam operator and the Fučík spectrum
The behavior of domain decomposition methods when the overlapping length is large
In this paper, we introduce a new approach for the convergence problem of optimized Schwarz methods by studying a generalization of these methods for a semilinear elliptic equation. We study the behavior of the algorithm when the overlapping length is large.
The block-grid method for solving Laplace's equation on polygons with nonanalytic boundary conditions.
The boundary element method with linear boundary elements for the Stokes flow.
The Cauchy problem for the homogeneous time-dependent Oseen system in : spatial decay of the velocity
We consider the homogeneous time-dependent Oseen system in the whole space . The initial data is assumed to behave as , and its gradient as , when tends to infinity, where is a fixed positive number. Then we show that the velocity decays according to the equation , and its spatial gradient decreases with the rate , for tending to infinity, uniformly with respect to the time variable . Since these decay rates are optimal even in the stationary case, they should also be the best possible...
The combination of approximate solutions for accelerating the convergence
The combination technique for a two-dimensional convection-diffusion problem with exponential layers
Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing for the maximum number of mesh intervals in each coordinate direction, our “combination” method simply adds or subtracts solutions that have been computed by the Galerkin FEM on , and meshes. It is shown that the combination FEM yields (up to a factor ) the same order of accuracy in the associated...
The Contraction Number of a Multigrid Method for Solving the Poisson Equation.
The Convergence of a Direct BEM for the Plane Mixed Boundary Value Problem of the Laplacian.
The convergence of a Galerkin approximation scheme for an extensible beam
The convergence of a new method for calculating lower bounds to eigenvalues
The Convergence of Even Degree Spline Collocation Solution for Potential Problems in Smooth Domains of the Plane.
The Convergence of Spline Collocation for Strongly Elliptic Equations on Curves.
The Convergence of two Numerical Schemes for the Navier-Stokes Equations.
The Convergence rate and Complexity of Precondotioned Iterative methods based on Approximate finite Element matrix Factorization
The density of solenoidal functions and the convergence of a dual finite element method
A proof is given of the following theorem: infinitely differentiable solenoidal vector - functions are dense in the space of functions, which are solenoidal in the distribution sense only. The theorem is utilized in proving the convergence of a dual finite element procedure for Dirichlet, Neumann and a mixed boundary value problem of a second order elliptic equation.
The Dependence of Critical Parameter Bounds on the Monotonicity of a Newton Sequence.
The difference method for non-linear elliptic differential equations with mixed derivatives
The discrete compactness property for anisotropic edge elements on polyhedral domains
We prove the discrete compactness property of the edge elements of any order on a class of anisotropically refined meshes on polyhedral domains. The meshes, made up of tetrahedra, have been introduced in [Th. Apel and S. Nicaise, Math. Meth. Appl. Sci. 21 (1998) 519–549]. They are appropriately graded near singular corners and edges of the polyhedron.
The discrete compactness property for anisotropic edge elements on polyhedral domains∗
We prove the discrete compactness property of the edge elements of any order on a class of anisotropically refined meshes on polyhedral domains. The meshes, made up of tetrahedra, have been introduced in [Th. Apel and S. Nicaise, Math. Meth. Appl. Sci. 21 (1998) 519–549]. They are appropriately graded near singular corners and edges of the polyhedron.