A C...-Collocation-like Method for Two-Point Boundary Value Problems.
A Collocation Method for Boundary Value Problems.
A comparison of four- and five-point difference approximations for stabilizing the one-dimensional stationary convection-diffusion equation.
A computational investigation of an integro-differential inequality with periodic potential.
A Convergent Finite Elemet Formulation for Transonic Flow.
A Finite Element Merthod Scheme for one Dimensional Elliptic Equations with High Super Convergence at the Nodes.
A Finite Element Method for a Singularly Perturbed Boundary Value Problem.
A Galerkin method of for singular boundary value problems.
A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations.
A method of discretization for the Lagerström-Cole model equation.
A mixed finite element method for Darcy flow in fractured porous media with non-matching grids
We consider an incompressible flow problem in a N-dimensional fractured porous domain (Darcy’s problem). The fracture is represented by a (N − 1)-dimensional interface, exchanging fluid with the surrounding media. In this paper we consider the lowest-order (ℝ T0, ℙ0) Raviart-Thomas mixed finite element method for the approximation of the coupled Darcy’s flows in the porous media and within the fracture, with independent meshes for the respective domains. This is achieved thanks to an enrichment...
A mixed finite element method for Darcy flow in fractured porous media with non-matching grids∗
We consider an incompressible flow problem in a N-dimensional fractured porous domain (Darcy’s problem). The fracture is represented by a (N − 1)-dimensional interface, exchanging fluid with the surrounding media. In this paper we consider the lowest-order (ℝ T0, ℙ0) Raviart-Thomas mixed finite element method for the approximation of the coupled Darcy’s flows in the porous media and within the fracture, with independent meshes for the respective...
A multilevel method with correction by aggregation for solving discrete elliptic problems
The author studies the behaviour of a multi-level method that combines the Jacobi iterations and the correction by aggragation of unknowns. Our considerations are restricted to a simple one-dimensional example, which allows us to employ the technique of the Fourier analysis. Despite of this restriction we are able to demonstrate differences between the behaviour of the algorithm considered and of multigrid methods employing interpolation instead of aggregation.
A numerical method for solution of semidifferential equations
A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems
A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation are presented and analyzed theoretically. The positive number is supposed to be much less than the discretization step and the values of . An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.
A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems
FEM discretizations of arbitrary order are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.
A simple proof of the spectral continuity of the Sturm-Liouville problem
The aim of this article is to present a simple proof of the theorem about perturbation of the Sturm-Liouville operator in Liouville normal form.
A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-finite domain.
A spectral regularization method for a Cauchy problem of the modified Helmholtz equation.
A Two Point Boundary Value Problem with a Rapidly Oscillating Solution.