Local maximum entropy (LME) meshfree basis functions are among the few approximants that possess the Kronecker delta property on the boundary, which enable to impose the essential boundary conditions directly like FEM. This study presents the potential of a meshfree method based on LME approximation for the Convection–Diffusion problem via well-celebrated SUPG. The present LME based Streamline Upwind Petrov–Galerkin meshfree method (SUPGM) benefits from the advantages emanated from both methods. LME approximants accounts for the disposal of the elements and direct imposition of boundary conditions and the SUPGM technique to deal with the issues associated with the non-self-adjoint convective term. Two standard benchmark problems are considered to validate the LME-SUPGM. The effect of different priors and radius of support that defines the LME basis are studied to test their importance in the present method. It is found that a balance between stability and accuracy is possible with ease by tuning the effective radius of support for LME for the given problem. The present method converges faster than FEM-SUPG and provides a smooth solution relatively.

局部最大熵 (LME) 无网格基函数是少数在边界上具有 Kronecker delta 属性的近似函数之一，它能够像 FEM 一样直接施加基本边界条件。本研究展示了基于 LME 近似的无网格方法通过广为人知的 SUPG 解决对流-扩散问题的潜力。目前基于 LME 的 Streamline Upwind Petrov-Galerkin meshfree 方法 (SUPGM) 受益于这两种方法的优点。LME 近似值考虑了元素的处理和边界条件的直接施加，以及 SUPGM 技术来处理与非自伴随对流项相关的问题。考虑了两个标准基准问题来验证 LME-SUPGM。研究了定义 LME 基础的不同先验和支持半径的影响，以测试它们在本方法中的重要性。我们发现，通过针对给定问题调整 LME 的有效支撑半径，可以轻松实现稳定性和准确性之间的平衡。本方法比 FEM-SUPG 收敛得更快，并提供了相对平滑的解决方案。