We study monotone P1 finite element methods on unstructured meshes for fully non-linear, degenerately parabolic Isaacs equations with isotropic diffusions arising from stochastic game theory and optimal control and show uniform convergence to the viscosity solution. Elliptic projections are used to manage singular behaviour at the boundary and to treat a violation of the consistency conditions from the framework by Barles and Souganidis by the numerical operators. Boundary conditions may be imposed in the viscosity or in the strong sense, or in a combination thereof. The presented monotone numerical method has well-posed finite dimensional systems, which can be solved efficiently with Howard's method.

翻译：我们研究单质P1 有限元素方法,用于无结构的模层,以完全非线性、退化的抛物线Isaac等方程式,通过随机游戏理论和最佳控制和最佳控制产生同位素扩散,并显示与粘度溶液的统一趋同; Elliptic 预测用于管理边界上的单一行为,并处理数字操作员Barles和Souganidis违反框架一致性条件的情况; 边界条件可以在粘性或强烈意义上,或结合使用。 提出的单质数字方法有完全保有的有限维度系统,可通过霍华德的方法有效解决。