Numerical Methods for Partial Differential Equations

Dear Colleagues,

Partial differential equations (PDE) are important mathematical models whose solutions are always hard to obtain. Therefore, solving partial differential equations numerically is of great significance and has application value in the field of scientific research and engineering applications. Many studies have been devoted to this problem, and the finite element methods, finite volume methods, and finite difference methods have been the most successful. However, the development of novel and efficient numerical method meets many challenges. Toward this end, our Topic seeks to contribute to the numerical approximation of PDEs in various science and engineering fields that focus on theoretical results describing robustness, stability, and convergence of the new methods. The Topic seeks to be interdisciplinary while emphasizing numerical analysis and approximation theory in the following areas of research:

• Discretization schemes for linear and nonlinear PDEs;
• Techniques for high-dimensional spatial PDEs;
• Learning algorithms for data-driven solutions to PDEs;
• New approaches for modeling complex phenomena with PDEs.

Prof. Dr. Pengzhan Huang
Prof. Dr. Yinnian He
Topic Editors