The Study On SUPG Method Solving Stokes Problems Upon Anisotropic Meshes

In terms of Stokes equations,after being endowed a discrete norm,discretization error can be bounded by the sum of interpolation errors and its first and second order derivatives.Some error analysis from other scholars is obtained by using isotropic grids and error estimations are expressed by means of the eigenvalues of matrix-es.In this manner,there are further improvements in both the breadth of content and practical operations.This article strives to simplify these error formulations yielded by using anisotropic meshes.In this way,we can enrich theoretical analysis and operations.The article applies to finite element space and geometric proper-ties of partitioned elements.The core method is the reference element technique,which constructs a affine mapping from reference element to anisotropic mesh.To yield corresponding metric tension and stabilization parameter,each element needs to follow shape,size,equi-distribution requirements.This article estimates the er-ror between numerical solution and the true one of Stokes equations,obtained by using SUPG method on anisotropic meshes.Meanwhile,we select the appropriate stabilization parameter and monitor function for using linear SUPG method to solve homogeneous Stokes equations.