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Тезисы докладов

Вычислительная алгебра

Let $Omegasubset R^2$ be a convex and bounded domain with a sufficiently regular boundary $Gamma$. The following minimization problem is considered, which describes laminar flow of visco-plastic fluid through a cross-section $Omega$: begin{equation} left{begin{array}{l} I(v)={1over 2}intlimits_{Omega}nabla ucdotnabla v,dOmega -intlimits_{Omega}fv,dOmega +g_1intlimits_{Omega}|nabla v|,dOmega +g_2intlimits_{Gamma}|v|,dGamma to minvin W_2^1(Omega), end{array}right. end{equation} where $g_1, g_2-const,~g_1, g_2>0$,~$fin L_2(Omega)$. The functional $I(v)$ is not differentiable and, at that, the kernel of the from $a(v,v)=intlimits_{Omega}|nabla v|^2,dOmega$ is non-trivial in the space $W_2^1(Omega)$. In order to avoid this difficulties a stable method, based on combining the iterative prox-regularization method with variational principles of duality, was constructed and substantiated. Estimation of error is defined for numerical solution of the problem in case of realization this algorithm on the basis of the finite elements method. The work is sustained by RFFI fund (grant 00-01-00754).

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