LaVa

The LaVa project, full title "The Latent Variable Proximal Point Method: A structure‐preserving approach to constrained variational problems", seeks to solve constrained variational problems wherever they appear.

New mathematical foundations will be developed and form a solution framework that will equip computational researchers with tools to develop highly accurate, scalable, higher order methods to solve problems relevant to understanding climate change, computational hydrology, and optimal control.

At the core of the approach lies a new nonlinear approximation method called the Latent Variable Proximal Point (LVPP) method. There will be a significant focus on mathematical rigor, which will be supported by computational experiments and publicly available code for fast dissemination.

• Objective 1: Provide a comprehensive numerical approach to structured elliptic variational inequalities based on the LVPP method covering theory, algorithms, applications, and scalable implementation.
• Objective 2: Extend the LVPP method to evolutionary variational inequalities leading to new timestepping, structure‐preserving methods with a focus on applications in hydrology and glaciology.
• Objective 3: Publish widely available open source implementations with accompanying tutorials for all numerical experiments emphasizing reproducibility.

Funding

This project is funded through the Research Council of Norway's FRIPRO scheme for Experienced Scientists with total funding of 12 million NOK.