【摘要】 基于广义拉格朗日乘子法,采用虚拟区域公式求解泊松边值问题.该方法的特点是所有的计算都是在辅助简单区域上进行的,原始区域嵌入到这个虚拟区域中.辅助区域的简单性使得可以用一致网格剖分构造有限元空间,产生具有特殊结构的刚度矩阵.数值实验表明,该方法随着网格的细化,相对误差越来越小,计算值越来越接近真解,计算值与真解的相对误差为0.177 585.更多还原

【Abstract】 Based on the essence of generalized Lagrange multiplier,a fictitious domain method,especially for Poisson problems,is proposed,where all computational tasks are carried out in an auxiliary simply shaped domain,and the original domain is embedded into.The simplicity of the auxiliary domain enables to use uniform meshes to construct the finite element space and deduce a distinguished stiffness matrix.The numerical solution expectively approaches the exact one as the grid gets finer,and the relative error reaches to 0.177 585.更多还原