Monge-Ampere 型方程的伪瞬态延拓和时间推进方法
Pseudo transient continuation and time marching methods for Monge-Ampere type equations
AI总结：
针对完全非线性椭圆 Monge-Ampere 方程，提出了伪瞬态延拓和纯伪时间推进两种数值方法，证明了其收敛到严格凸解，并给出了离散问题严格凸解存在性的证明与数值验证。
摘要：
我们提出了完全非线性椭圆 Monge-Ampere 方程的两种数值方法。第一种是伪瞬态延拓方法，第二种是纯伪时间推进方法。这些方法被证明收敛到自然离散变分公式的严格凸解，该公式采用 $C^1$ 协调逼近。对于连续问题的光滑解，证明了离散问题严格凸解的存在性，并通过数值证据支持了非光滑解的情况。
英文摘要：
We present two numerical methods for the fully nonlinear elliptic Monge-Ampere equation. The first is a pseudo transient continuation method and the second is a pure pseudo time marching method. The methods are proven to converge to a strictly convex solution of a natural discrete variational formulation with $C^1$ conforming approximations. The assumption of existence of a strictly convex solution to the discrete problem is proven for smooth solutions of the continuous problem and supported by numerical evidence for non smooth solutions.
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