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Displaying 361 –
380 of
407
For an elliptic model problem with non-homogeneous unilateral boundary conditions, two dual variational formulations are presented and justified on the basis of a saddle point theorem. Using piecewise linear finite element models on the triangulation of the given domain, dual numerical procedures are proposed. By means of one-sided approximations, some a priori error estimates are proved, assuming that the solution is sufficiently smooth. A posteriori error estimates and two-sided bounds for the...
A model second order elliptic equation in cylindrical coordinates with mixed boundary conditions is considered. A dual variational formulation is employed to calculate the cogradient of the solution directly. Approximations are defined on the basis of standard finite elements spaces. Convergence analysis and some a posteriori error estimates are presented.
The paper presents a problem of duality for the obstacle and unilateral biharmonic problem (the equilibrium of a thin plate with an obstacle inside the domain or on the boundary). The dual variational inequality is derived by introducing polar functions.
A mixed finite element method for the Navier–Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier–Stokes equations and the classical theory extends naturally to this setting. Finite element spaces satisfying the associated inf–sup conditions are developed.
Dubrovin type equations for the N -gap solution of a completely
integrable system associated with a polynomial pencil is constructed and
then integrated to a system of functional equations. The approach used to
derive those results is a generalization of the familiar process of finding the
1-soliton (1-gap) solution by integrating the ODE obtained from the soliton
equation via the substitution u = u(x + λt).
We consider a two-player zero-sum-game in a bounded open domain Ω
described as follows: at a point x ∈ Ω, Players I and II
play an ε-step tug-of-war game with probability α, and
with probability β (α + β = 1), a
random point in the ball of radius ε centered at x is
chosen. Once the game position reaches the boundary, Player II pays Player I the amount
given by a fixed payoff function F. We give a detailed proof of the fact
that...
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