Auxiliary Space Preconditioners for a $$C^{0}$$ Finite Element Approximation of Hamilton–Jacobi–Bellman Equations with Cordes Coefficients

In the past decade, there are many works on finite element methods for fully nonlinear Hamilton–Jacobi–Bellman (HJB) equations with Cordes condition. The linearised systems have large condition numbers, which depend not only mesh size but also parameters in This paper is concerned design and analysis of auxiliary space preconditioners a $$C^0$$ discretization HJB [Calcolo, 58, 2021]. Based stable decomposition spaces, we propose both additive multiplicative converge uniformly sense that resulting number independent degrees freedom parameter $$\lambda $$ Numerical experiments carried out to illustrate efficiency proposed preconditioners.