A note on polynomial approximation in Sobolev spaces
A note on polynomial approximation in Sobolev spaces
For domains which are star-shaped w.r.t. at least one point, we give new bounds on the constants in Jackson-inequalities in Sobolev spaces. For convex domains, these bounds do not depend on the eccentricity. For non-convex domains with a re-entrant corner, the bounds are uniform w.r.t. the exterior angle. The main tool is a new projection operator onto the space of polynomials.
A note on the approximation of free boundaries by finite element methods
A Note on the Approximation of Mildly Nonlinear Dirichlet Problems by Finite Differences.
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 the Numerical Solution of a Fourth-Order Parabolic Partial Differential Equation
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 algorithm for the Stokes problem based on an integral equation for the pressure via conformal mappings.
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 elliptic problems.
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 solution of the Dirichlet problem on some special doubly connected regions
The aim of this paper is to give a convergence proof of a numerical method for the Dirichlet problem on doubly connected plane regions using the method of reflection across the exterior boundary curve (which is analytic) combined with integral equations extended over the interior boundary curve (which may be irregular with infinitely many angular points).
A numerical study of eigenvalues of the hyperbolic Laplacian for polyhedra with one cusp.