A local projection stabilization/continuous Galerkin--Petrov method for incompressible flow problems
- Ahmed, Naveed
- John, Volker
- Matthies, Gunar
- Novo, Julia
2010 Mathematics Subject Classification
- 65M12 65M15 65M80
- Evolutionary Oseen problem, inf-sup stable pairs of finite element spaces, local projection stabilization (LPS) methods, continuous Galerkin--Petrov (cGP) methods
The local projection stabilization (LPS) method in space is consid-ered to approximate the evolutionary Oseen equations. Optimal error bounds independent of the viscosity parameter are obtained in the continuous-in-time case for the approximations of both velocity and pressure. In addition, the fully discrete case in combination with higher order continuous Galerkin--Petrov (cGP) methods is studied. Error estimates of order k + 1 are proved, where k denotes the polynomial degree in time, assuming that the convective term is time-independent. Numerical results show that the predicted order is also achieved in the general case of time-dependent convective terms.
- Appl. Math. Comput., 333 (2018), pp. 304--324, DOI 10.1016/j.amc.2018.03.088 .