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.

中文翻译：

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具有粘性和强狄利克雷边界条件的各向同性Isaacs方程的有限元方法

我们研究了非结构网格上的单调P1有限元方法，它是由随机博弈论和最优控制引起的具有各向同性扩散的完全非线性，退化抛物线Isaacs方程，并且显示出对粘度解的一致收敛。椭圆投影用于管理边界处的奇异行为，并由数值算子处理Barles和Souganidis提出的违反一致性条件的情况。可以以粘度或强意义或它们的组合施加边界条件。提出的单调数值方法具有良好的有限维系统，可以用霍华德方法有效地求解。