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Numerical Methods for Partial Differential Equations is an international journal that publishes the highest quality research in the rigorous analysis of novel techniques for the numerical solution of partial differential equations (PDEs).The journal is intended to be accessible to a broad spectrum of researchers into numerical approximation of PDEs throughout science and engineering, with priority given to articles that focus on theoretical results describing robustness, stability, and convergence of the new methods rather than the techniques themselves and specific applications.The Journal seeks to be interdisciplinary, while emphasizing numerical analysis and approximation theory in the following areas of research: discretization schemes for linear, nonlinear, and fractional PDEs; methods for optimal control and parameter estimation problems; techniques for high-dimensional spatial and parameterized PDEs; learning algorithms for data-driven solutions to PDEs; and new approaches for modeling complex phenomena with PDEs.