Analysis of finite dimensional approximations to a class of partial differential equations | Zendy

Bao Gang | Zendy; Zhou Aihui | Zendy

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Analysis of finite dimensional approximations to a class of partial differential equations

Author(s) -

Bao Gang,

Zhou Aihui

Publication year - 2004

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.539

Subject(s) - mathematics , partial differential equation , finite element method , numerical partial differential equations , boundary value problem , convergence (economics) , class (philosophy) , mathematical analysis , simple (philosophy) , multigrid method , computer science , philosophy , physics , epistemology , artificial intelligence , economics , thermodynamics , economic growth

In this paper, a unified approach for analysing finite dimensional approximations to a class of partial differential equations boundary value problems (second‐kind Fredholm differential equations) is introduced. The approach is shown to be general despite of its extremely simple form. In particular, it is expected to be useful in the convergence analysis of finite element methods for solving PDE problems. Three specific examples are presented to illustrate the broad applicability of the approach. Copyright © 2004 John Wiley & Sons, Ltd.

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