An enriched Galerkin-characteristics finite element method for convection-dominated and transport problems

We propose an enriched Galerkin-characteristics finite element method for numerical solution of convection-dominated problems. The uses the modified characteristics integration total derivative in time, combined with spatial discretization on unstructured grids. L 2 -projection is implemented evaluation solutions by tracking departure points from each element. In present study, a family quadrature rules are used to enrich approximation integrals method. use as enrichment procedure allows discretizations coarse fixed meshes and no need introduce time-dependent enrichments. This offers very great advantage over conventional since same governing matrix representation can be during entire time steeping process. also multilevel adaptive monitoring gradient computational domain its advection. comparison traditional analysis h -, p - hp -version refinements, approach much simpler, more robust efficient, it yields accurate number degrees freedom without refining mesh. To examine performance proposed we solve several test examples convection-diffusion Comparison carried out work. aim such compared classical problems efficiently appropriate level accuracy.