Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations.
Two new finite difference methods for computing eigenvalues of a fourth order linear boundary value problem.
Two Numerical Methods for the elliptic Monge-Ampère equation
The numerical solution of the elliptic Monge-Ampère Partial Differential Equation has been a subject of increasing interest recently [Glowinski, in 6th International Congress on Industrial and Applied Mathematics, ICIAM 07, Invited Lectures (2009) 155–192; Oliker and Prussner, Numer. Math.54 (1988) 271–293; Oberman, Discrete Contin. Dyn. Syst. Ser. B10 (2008) 221–238; Dean and Glowinski, in Partial differential equations, Comput. Methods Appl. Sci. 16 (2008) 43–63; Glowinski et al., Japan...
Two one-step methods to solve the initial value problem
Two preconditioners based on the multi-level splitting of finite element spaces.
Two shape preserving Lagrange ...-interpolants.
Two sharp inequalities of Simpson type and applications.
Two simple derivations of universal bounds for the C.B.S. inequality constant
Universal bounds for the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for piecewise linear-linear and piecewise quadratic-linear finite element spaces in 2 space dimensions are derived. The bounds hold for arbitrary shaped triangles, or equivalently, arbitrary matrix coefficients for both the scalar diffusion problems and the elasticity theory equations.
Two step extrapolation and optimum choice of relaxation factor of the extrapolated S.O.R. method
Limits of the extrapolation coefficients are rational functions of several poles with the largest moduli of the resolvent operator and therefore good estimates of these poles could be calculated from these coefficients. The calculation is very easy for the case of two coefficients and its practical effect in finite dimensional space is considerable. The results are used for acceleration of S.O.R. method.
Two-dimensional Legendre wavelets and operational matrices of integration.
Two-grid finite-element schemes for the steady Navier-Stokes problem in polyhedra.
Two-grid finite-element schemes for the transient Navier-Stokes problem
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size . In the second step, the problem is linearized by substituting into the non-linear term, the velocity computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size . This approach is motivated by the fact that,...
Two-grid finite-element schemes for the transient Navier-Stokes problem
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size H. In the second step, the problem is linearized by substituting into the non-linear term, the velocity uH computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size h. This approach is motivated by the fact that,...
Two-level additive Schwarz preconditioners for fourth-order mixed methods.
Two-level nonlinear elimination based preconditioners for inexact Newton methods with application in shocked duct flow calculation.
Two-level stabilized nonconforming finite element method for the Stokes equations
In this article, we present a new two-level stabilized nonconforming finite elements method for the two dimensional Stokes problem. This method is based on a local Gauss integration technique and the mixed nonconforming finite element of the pair (nonconforming linear element for the velocity, conforming linear element for the pressure). The two-level stabilized finite element method involves solving a small stabilized Stokes problem on a coarse mesh with mesh size and a large stabilized Stokes...
Two-scale FEM for homogenization problems
The convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale is analyzed. Full elliptic regularity independent of is shown when the solution is viewed as mapping from the slow into the fast scale. Two-scale FE spaces which are able to resolve the scale of the solution with work independent of and without analytical homogenization are introduced. Robust in error estimates for the two-scale FE spaces are proved....
Two-scale FEM for homogenization problems
The convergence of a two-scale FEM for elliptic problems in divergence form with coefficients and geometries oscillating at length scale ε << 1 is analyzed. Full elliptic regularity independent of ε is shown when the solution is viewed as mapping from the slow into the fast scale. Two-scale FE spaces which are able to resolve the ε scale of the solution with work independent of ε and without analytical homogenization are introduced. Robust in ε error estimates for the two-scale FE spaces...
Two-sided a posteriori error estimates for linear elliptic problems with mixed boundary conditions
The paper is devoted to verification of accuracy of approximate solutions obtained in computer simulations. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. A mathematical model consisting of a linear elliptic (reaction-diffusion) equation with a mixed Dirichlet/Neumann/Robin boundary condition is considered...
Two-sided approximation to periodic solutions of ordinary differential equations.