A posteriori error estimates of mixed DG finite element methods for linear parabolic equations

Abstract

In this article, we analyse a posteriori error estimates of mixed finite element discretizations for linear parabolic equations. The space discretization is done using the order λ ≥ 1 Raviart–Thomas mixed finite elements, whereas the time discretization is based on discontinuous Galerkin (DG) methods (r ≥ 1). Using the duality argument, we derive a posteriori l ^∞(L ²) error estimates for the scalar function, assuming that only the underlying mesh is static.

Keywords:

• a posteriori error estimates
• mixed finite element
• discontinuous Galerkin methods
• parabolic equations

AMS Subject Classifications::

• 35K10
• 65N30