Titlebook: Elliptic Differential Equations; Theory and Numerical Wolfgang Hackbusch Book 2017Latest edition Springer-Verlag GmbH Germany 2017 differen

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书目名称Elliptic Differential Equations影响因子(影响力)




书目名称Elliptic Differential Equations影响因子(影响力)学科排名




书目名称Elliptic Differential Equations网络公开度




书目名称Elliptic Differential Equations网络公开度学科排名




书目名称Elliptic Differential Equations被引频次




书目名称Elliptic Differential Equations被引频次学科排名




书目名称Elliptic Differential Equations年度引用




书目名称Elliptic Differential Equations年度引用学科排名




书目名称Elliptic Differential Equations读者反馈




书目名称Elliptic Differential Equations读者反馈学科排名

angina-pectoris

The Poisson Equation,tation (3.6) of the solution, provided it is existing. Concerning the existence, Theorem 3.13 contains a negative statement (cf. .): The Poisson equation with a continuous right-hand side . may possess no classical solution. A sufficient condition for a classical solution is the Hölder continuity of

宏伟

Difference Methods for the Poisson Equation,sson equation .. This simple example is chosen to show the generation of the discrete system of equations. The difference equations are complemented by the Dirichlet boundary condition. The equations of the resulting linear system correspond to the inner grid points, while the boundary data appear i

Adulate

General Boundary-Value Problems,tement is the maximum-minimum principle in §5.1.2. In §5.1.3 sufficient conditions for the uniqueness of the solution and the continuous dependence on the data are proved. The discretisation of the general differential equation in a square is described in §5.1.4. Section 5.2 treats alternative bound

murmur

Tools from Functional Analysis,paces as well as the operators as linear and bounded mappings between these spaces. In most of the later applications these spaces will be function spaces, containing for instance the solutions of the differential equations. It will turn out that the Sobolev spaces from Section 6.2 are well suited f

果核

Variational Formulation,ces another approach via a variational problem (Dirichlet’s principle). Combining the variational formulation with the Sobolev spaces will be successful. In Section 7.2 the boundary-value problem of order 2. with homogeneous Dirichlet conditions is transferred into the variational formulation in the

果核

The Finite-Element Method,rmulation is extremely important for numerical purposes. It establishes a new, very flexible discretisation method. After historical remarks in Section 8.1 we introduce the Ritz–Galerkin method in Section 8.2. The basic principle is the replacement of the function space . in the variational formulat

minion

Immortal

GRIN

Elliptic Eigenvalue Problems, some basic terms are discussed in Section 11.1. Since we do not require the system to be symmetric, also the adjoint problem must be treated. Section 11.2 is devoted to the finite-element discretisation by a family . of subspaces. Theorems 11.13 and 11.15 state an important result: Each eigenvalue