Principles of Mimetic Discretizations of Differential Operators

  title={Principles of Mimetic Discretizations of Differential Operators},
  author={Pavel B. Bochev and James Mac Hyman},
Compatible discretizations transform partial differential equations to discrete algebraic problems that mimic fundamental properties of the continuum equations. We provide a common framework for mimetic discretizations using algebraic topology to guide our analysis. The framework and all attendant discrete structures are put together by using two basic mappings between differential forms and cochains. The key concept of the framework is a natural inner product on cochains which induces a… CONTINUE READING
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