一类非线性抛物方程的直接间断有限元方法  

The Direct Discontinuous Finite Element Method for a Type of Nonlinear Parabolic Equation

作　　者：王灿 郑云英[1] 赵振刚 WANG Can;ZHENG Yunying;ZHAO Zhengang(School of Mathematical Sciences,Huaibei Normal University,235000,Huaibei,Anhui,China;Department of Fundamental Courses,Shanghai Customs College,201204,Shanghai,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000 [2]上海海关学院公共教学部,上海201204

出　　处：《淮北师范大学学报（自然科学版）》2023年第1期8-15,共8页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省高校自然科学基金(KJ2018A0385);上海自然科学基金(19ZR1422000);安徽省自然科学基金(2008085MA11)。

摘　　要：文章针对一类非线性抛物方程构造全离散数值格式,在空间方向采用直接间断有限元方法,在时间方向利用修正的Crank-Nicolson格式。基于双线性算子强制性与连续性的详细讨论,得到全离散格式数值解的存在唯一性。随后的误差分析表明在能量范数下的最优结果为O(h^(2)+hΔt+Δt^(2)),并用数值算例验证该方法的有效性和理论结果。In this paper,a fullydiscrete numerical scheme is constructed for a class of nonlinear parabolic equations,with the direct discontinuous finite element method in space axis and the modified Crank-Nicolson method in time axis.Then,the coercivity and the continuity of bilinear operators are discussed in detail,and the existence and uniqueness of numerical solution for the fully discrete scheme can be gotten.The error estimate of modified Crank-Nicolson/DDG scheme is analyzed in detail. The results show that the optimal result under the energy norm is O(h^(2)+ hΔt + Δt^(2)). Numerical experiments are presented to demonstrate the theoretical results and effectiveness.

关 键 词：非线性抛物方程 直接间断有限元方法 修正的Crank-Nicolson格式 误差分析 

分 类 号：O241.82[理学—计算数学]