非线性发展方程的无网格比高精度有限元方法

UNCONDITIONAL HIGH ACCURACY FINITE ELEMENT METHODS FOR NONLINEAR EVOLUTION EQUATIONS

对于几类非线性的发展型方程——非线性抛物方程、非线性Schr?dinger方程、非线性Sobolev方程、非线性双曲方程,本文从协调有限元方法、非协调有限元方法、混合有限元方法等不同角度,利用不同技巧深入系统地研究了其线性化的全离散格式的构造、无网格比约束下的超逼近和超收敛分析.

Some nonlinear evolution equations, such as nonlinear parabolic equations,nonlinear Schrodinger equations, nonlinear Sobolev equations and nonlinear hyperbolic equations are studied deeply from different points of view and different techniques by conforming finite element method, nonconforming finite element method and mixed finite element method. Based on the research about the construction of linearized full discrete schemes, the unconditional superclose and superconvergent results are obtained.