We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using H(div)-conforming finite element methods, for which we prove error estimates for the velocity approximation in the L2-norm of order O(hk+1/2). We also prove error estimates for the pressure error in the L2-norm.
|Journal||Mathematical Models and Methods in Applied Sciences|
|Publication status||Accepted/In press - 14 Jan 2020|
- inviscid flows
- error estimates
- H(div) conforming finite elements
Barrenechea, G., Burman, E., & Guzman, J. (Accepted/In press). Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow. Mathematical Models and Methods in Applied Sciences.