Brown University received a $400,000 Project Grant award from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049). The award will fund research from July 1, 2023 through June 30, 2026 to develop efficient numerical methods for solving partial differential equations. Specifically, Brown University researchers will investigate algorithm development, analysis and application of high-order numerical methods including discontinuous Galerkin finite element and weighted essentially non-oscillatory finite difference/volume schemes. The algorithms will be designed to solve linear and nonlinear convection-dominated PDEs with an emphasis on bound preserving techniques, moving boundaries, stochastic effects and efficient time discretization. Workforce development for underrepresented STEM students is also included. The research aims to provide guidance on algorithm applicability/limitations while enhancing accuracy, stability and robustness. Collaborations with engineers and applied scientists are planned to enable efficient application of new/existing algorithms. This award supports the NSF's mission to promote mathematical and physical sciences progress through strengthening the Nation's scientific enterprise.