A Three-Dimensional Moving Finite Element Method Based On A Posteriori Error Estimation.

Abstract

A moving finite element method based on a posteriori error estimate is presented
for three-dimensional compressible flows, with emphasis on shock waves. The adaptation
procedure uses an interpolation error estimate whose magnitude and direction are controlled
by the Hessian, containing second derivatives of the specific mass. This error is projected
over mesh edges and drive the nodal movement scheme to satisfy an optimal mesh criterion.
While traditionally the optimal mesh criterion is one in which the error is equidistributed
over the elements, in this work the error is equidistributed over the edges. Mesh anisotropy is
avoided employing a formulation based in variational principles. Finally, numerical result
obtained with current method are presented and analyzed for several examples.