A note on the effect of numerical quadrature in finite element eigenvalue approximation.
A note on the efficiency of residual-based a posteriori error estimators for some mixed finite element methods.
A note on variational discretization of elliptic Neumann boundary control
A note to Friedrichs' inequality
A novel approach to modelling of flow in fractured porous medium
There are many problems of groundwater flow in a disrupted rock massifs that should be modelled using numerical models. It can be done via “standard approaches” such as increase of the permeability of the porous medium to account the fracture system (or double-porosity models), or discrete stochastic fracture network models. Both of these approaches appear to have their constraints and limitations, which make them unsuitable for the large- scale long-time hydrogeological calculations. In the article,...
A numerical approach to a class of unilateral elliptic problems of non-variational type
A numerical method for detecting singular minimizers of multidimensional problems in nonlinear elasticity.
A numerical method for the solution of the nonlinear observer problem
The central part in the process of solving the observer problem for nonlinear systems is to find a solution of a partial differential equation of first order. The original method proposed to solve this equation used expansions into Taylor polynomials, however, it suffers from rather restrictive assumptions while the approach proposed here allows to generalize these requirements. Its characteristic feature is that it is based on the application of the Finite Element Method. An illustrating example...
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 of a two-dimensional transport equation
In this paper we present a variational method for approximating solutions of the Dirichlet problem for the neutron transport equation in the stationary case. Error estimates from numerical examples are used to evaluate an approximation of the solution with respect to the steps of two grids.
A numerical study of eigenvalues of the hyperbolic Laplacian for polyhedra with one cusp.
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 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 penalty method for approximations of the stationary power-law Stokes problem.
A Penalty Method for the Approximate Solution of Stationary Maxwell Equations.