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1) Taylor expansions, central differences
expressions, backwards differences
expressions, forward
difference equations, finite difference
schemes for boundary value problems,
truncation errors,
stability, consistence and convergence.
2) Generalized inner products, discrete
Green identity, staggered grid,
mimetic gradient operator,
divergence gradient operator, mimetic
boundary operators.
3) General mimetic discretization
of second order elliptic problems,
examples of specific mimetic
discretizations for static diffusion
equation and Poisson equations.
4) Associated conservative schemes,
approximation theorem for mimetic
and conservative
schemes, and convergence of conservative
and mimetic schemes.
5) Applications of mimetic schemes
for solving the Poisson equation,
biharmonic equation, and
pressure equations in porous media
flow.
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1) Castillo J.E. and Grone R. “A
matrix analysis to higher order
approximations for divergences
and gradients satisfying a global
conservation law”. SIAM Journal
of Matrix Analysis
Applications. (2004).
2) Castillo J.E. and Yasuda M. “”Linear
system arising for second order
mimetic divergence and
gradient discretizations”,
Journal of Mathematical Modelling
and Algorithms. (2005).
3) Guevara-Jordan J.M., Rojas S.,
Freites-Villegas M., Castillo J.E.
“Convergence of a mimetic
finite differences method for the
static diffusion equation”.
Advances in Differences Equations.
(2007).
4) Guevara-Jordan J.M., Rojas S.,
Freites-Villegas M., Castillo J.E.
“A new second order finite
difference conservative scheme”.
Divulgaciones Matemáticas.
(2005).
5) Guevara-Jordan J.M. and Arteaga-Arispe
J. “A second order mimetic
approach for tracer flow
in oil reservoirs”. Society
of Petroleum Engineers paper SPE
107366. (2007).
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