This paper deals with the numerical approximation of solutions of Stokes and Brinkman systems using meshless methods. The aim is to solve a problem containing a nonzero body force, starting from the well known decomposition in terms of a particular solution and the solution of a homogeneous force problem. We propose two methods for the numerical construction of a particular solution. One method is based on the Neuber-Papkovich potentials, which we extend to nonhomogeneous Brinkman problems. A second method relies on a Helmholtz-type decomposition for the body force and enables the construction of divergence-free basis functions. Such basis functions are obtained from Hänkel functions and justified by new density results for the space H¹(Ω). Several 2D numerical experiments are presented in order to discuss the feasibility and accuracy of both methods.

本文处理使用无网格方法的 Stokes 和 Brinkman 系统解的数值逼近。目的是解决一个包含非零体力的问题，从众所周知的分解开始，根据特定解和齐次力问题的解。我们提出了两种数值构造特定解的方法。一种方法是基于 Neuber-Papkovich 势，我们将其扩展到非齐次 Brinkman 问题。第二种方法依赖于体力的亥姆霍兹型分解，并能够构建无散基函数。这样的基函数是从 Hänkel 函数获得的，并由空间H ^{1的新密度结果证明}(Ω)。为了讨论这两种方法的可行性和准确性，提出了几个二维数值实验。