Manuscript Topics

Numerical methods for solving partial differential equations are needed in practice since only a few differential equations can be mathematically solved. The goal of this Special Issue is to provide an overview of the recent progress in using numerical methods to solve partial differential equations. These include finite difference methods; finite element methods and their extensions, including discontinuous Galerkin (DG) methods devoted to approximate the solutions for various real-world problems, such as fluid flow, solid mechanics, electromagnetics, and many others, as well as the analysis of these methods including error estimation, superconvergence, and adaptivity. Other topics include the design and analysis of new numerical schemes, as well as novel applications in any branch of engineering and science. While all contributions related to numerical methods are invited, the featured topics include: stability issues, efficient time integration, superconvergence phenomena, a priori and a posteriori error estimations, and mesh adaptivity. Contributions dealing with the applications of numerical methods for porous media flow, incompressible flow, solid mechanics, and elasticity are welcome.

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