Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and general unbounded domains, linear elliptic problems with a parameter for mixed order systems, infinite-dimensional Schrodinger equations, Navier-Stokes equations, and nonlinear Maxwellequations. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplecticgeometry. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. This book celebrates Vishik's eightieth birthday. However, the implementation of meshfree methods and their parallelization also requires special attention, for instance with respect to numerical integration.Äescription: Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. Furthermore, meshfree methods have a number of advantageous features that are especially attractive when dealing with multiscale phenomena: A-priori knowledge about the solution’s particular local behavior can easily be introduced into the meshfree approximation space, and coarse scale approximations can be seamlessly refined by adding fine scale information. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. Description: There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s.
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