Abstract
A mixed finite element approximation of $H^2$ solutions to the fully nonlinear Hamilton--Jacobi--Bellman equation, with coefficients that satisfy the Cordes condition, is proposed and analyzed. A priori and a posteriori bounds on the approximation error are proved. The contributions from the a posteriori error estimator can be used as refinement indicators in an adaptive mesh-refinement algorithm. The convergence of this procedure is proved and empirically studied in numerical experiments
Original language | English |
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Pages (from-to) | 592-614 |
Number of pages | 23 |
Journal | SIAM journal on numerical analysis |
Volume | 57 |
Issue number | 2 |
DOIs | |
Publication status | Published - 19 Mar 2019 |