کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
499102 | 863027 | 2009 | 16 صفحه PDF | دانلود رایگان |
We present a new theoretical framework for the enforcement of constraints in variational multiscale (VMS) analysis. The theory is first presented in an abstract operator format and subsequently specialized for the steady advection–diffusion equation. The approach borrows heavily from results in constrained and convex optimization. An exact expression for the fine-scales is derived in terms of variational derivatives of the constraints, Lagrange multipliers, and a fine-scale Green’s function. The methodology described enables the development of numerical methods which satisfy predefined attributes. A practical and effective procedure for solving the steady advection–diffusion equation is presented based on a VMS-inspired stabilized method, weakly enforced Dirichlet boundary conditions, and enforcement of a maximum principle and conservation constraint.
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 199, Issues 1–4, 1 December 2009, Pages 61–76