High Order Mimetic Discretizations of Continuum Mechanics 

Dr. Jose E. Castillo,
 Computational Science Research Center, San Diego State University 

Abstract: Mimetic Operators
satisfy a discrete analog of the divergence theorem and they are used
to create/design conservative/reliable numerical representations to
continuous models. We will present a methodology to construct mimetic
versions of the divergence and gradient operators which exhibit high
order of accuracy at the grid interior as well as at the
boundaries. As a case of study, we will show the construction of
fourth order operators in a one-dimensional staggered grid. Mimetic
conditions on discrete operators are stated using matrix analysis and
the overall high order of accuracy determines the bandwidth
parameter. This contributes to a marked clarity with respect to
earlier approaches of construction. As test cases, we will solve 2-D
elliptic equations with full tensor coefficients arising from oil
reservoir models. Additionally, applications to elastic wave
propagation under free surface and shear rupture boundary conditions
will be given.