Saddle point least squares for the reaction–diffusion problem

Results in Applied Mathematics

Jacob Jacavage¹  Constantin Bacuta² 

[1] Corresponding author.;University of Delaware, Mathematical Sciences, 501 Ewing Hall, Newark, DE 19716, United States of America;

关键词: Least squares;    Saddle point systems;    Mixed methods;    Multilevel methods;    Uzawa algorithm;    Conjugate gradient;   

DOI  :  

来源: DOAJ

【 摘 要 】

We consider a mixed variational formulation for the reaction–diffusion problem based on a saddle point least square approach with an optimal test norm and nonconforming trial spaces. An Uzawa type iterative process for solving the discrete mixed formulations is proposed and choices for discrete stable spaces are provided. The implementation requires a nodal basis only for the test space, and assembly of a global saddle point system is avoided. For the test space, we use piecewise linear spaces of functions on Shishkin type meshes that provide almost optimal approximation in the standard symmetric elliptic formulation. Our saddle point least squares method has the advantage that the order of approximation of the solution in a balanced norm is improved if compared with the standard variational approach. Numerical results are included to support the proposed method.

【 授权许可】

Unknown