稳定渗流分析的局部间断伽辽金有限元法

针对稳定渗流分析问题的特征,依据局部间断伽辽金有限元法原理,推导出稳定渗流分析问题的局部间断迦辽金有限元法基本计算格式,并对该计算格式的有效性进行探讨.通过分析基本计算格式相应的变分形式,考虑变分形式中双线性算子的稳定性及有界性,利用Lax-Milgram定理论证这一基本计算格式解的存在性、唯一性,从而证明局部间断伽辽金有限元法可以用来处理稳定渗流分析问题.通过对该格式的解进行先验误差分析,证明其近似解具有p+1阶的精度,表明相对于一般的有限元法来说,局部间断伽辽金有限元法是一种高精度的数值计算方法.

Local discontinuous Galerkin finite element method for steady seepage analysis

Based on the characteristics of the steady seepage equation,a basic calculation formula of the local discontinuous Galerkin finite element method for steady seepage analysis was deduced according to the principle of the method,and the feasibility of the formula was studied.The variational formula of the basic formula was analyzed with consideration of the stability and boundedness of the bilinear operator in the variational formula.The Lax-Milgram theorem was used to verify the existence and uniqueness of the solution of the basic formula,in order to demonstrate that the local discontinuous Galerkin finite element method is applicable to steady seepage analysis.Through a priori error analysis,the formula was proved to have p+1-order accurate approximations,indicating that the local discontinuous Galerkin finite element method is a high-precision numerical method compared with commonly used finite element methods.