论文标题
低规律性的原始双重弱熟练的gallkin有限元方法，用于椭圆形的cauchy问题
Low Regularity Primal-Dual Weak Galerkin Finite Element Methods for Ill-Posed Elliptic Cauchy Problems
论文作者
论文摘要
引入和分析了一种新的原始双弱弱彩手（PDWG）有限元方法，并分析了在精确溶液上具有超低规律性假设的椭圆形的cauchy问题。由PDWG方案产生的Euler-Lagrange公式产生了涉及原始方程和伴随方程的方程式系统。建立了低规律性假设中原始变量的最佳顺序误差估计。说明了一系列数值实验以验证开发理论的有效性。
A new primal-dual weak Galerkin (PDWG) finite element method is introduced and analyzed for the ill-posed elliptic Cauchy problems with ultra-low regularity assumptions on the exact solution. The Euler-Lagrange formulation resulting from the PDWG scheme yields a system of equations involving both the primal equation and the adjoint (dual) equation. The optimal order error estimate for the primal variable in a low regularity assumption is established. A series of numerical experiments are illustrated to validate effectiveness of the developed theory.
