A new numerical analysis for partial differential equations with noise

带有噪声的偏微分方程的新数值分析

• 批准号: DP220100937
• 负责人: Dr Kim Ngan Le
• 金额: $ 28.38万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-03-22 至 2026-03-21
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP220100937
• 关键词: new; numerical; analysis; partial; differential

This project aims to design novel numerical methods, grounded in rigorous mathematical foundations, for partial differential equations with stochastic source terms, such as for instance those modelling fluid flows with random perturbations. To ensure the accuracy of numerical simulations, preserving certain quantities of importance (mass, flux) is critical. The project's goal is to develop finite volume and high-order numerical methods that are applicable in real-world settings, designed to achieve this preservation of essential quantities, and mathematically proven to be robust. The expected benefits are cost-efficient and reliable numerical tools for the scientific simulation of phenomena subjected to uncontrolled influence.

该项目旨在设计新的数值方法，建立在严格的数学基础上，用于具有随机源项的偏微分方程，例如那些模拟具有随机扰动的流体流动的方法。为了确保数值模拟的准确性，保留某些重要的量（质量，通量）是至关重要的。该项目的目标是开发适用于现实世界环境的有限体积和高阶数值方法，旨在实现基本数量的保存，并在数学上证明是稳健的。预期的好处是具有成本效益和可靠的数值工具的科学模拟现象受到不受控制的影响。