Node Reconnection Algorithm for Mimetic Finite Difference Discretization of Elliptic Equations

Markus Berndt berndt@cut.this.part.lanl.gov

Konstantin Lipnikov lipnikov@cut.this.part.lanl.gov

Pavel Vachal vachal@cut.this.part.galileo.fjfi.cvut.cz

Mikhail Shashkov shashkov@cut.this.part.lanl.gov

Most efficient adaptive mesh methods employ only a few strategies, including local mesh refinement (h-adaptation), movement of mesh nodes (r-adaptation), and node reconnection (c-adaptation). Despite its simplicity, node reconnection is the least popular of the three. However, using only node reconnection, the discretization error can be significantly reduced.

We developed and numerically analyzed a new c-adaptation algorithm for mimetic finite difference discretizations of elliptic equations on triangular meshes. Numerical results show that even the change of a few edges based on our strategy can greatly improve the solution.