Combining Galerkin matrix perturbation with Taylor weak statement algorithms
For a large class of computational fluid dynamics (CFD) problems, the discrete approximate solution error is viewed as truncation of a Taylor series expansion. In this paper, a recently developed weak statement Galerkin Matrix Perturbation (GMP) method, is theoretically compared and combined with the well known Taylor Weak Statement (TWS) algorithm on a term by term basis yielding simple tridiagonal forms that reduce, or annihilate in special cases, the Taylor series truncation error. Verification hyperbolic solution is documented for a linear smooth and non-smooth incompressible wave cluster propagation using a combination algorithm of GMP and TWS.
matrix perturbation taylor weak statement finite element static condensation high order accurate fully discrete