Error estimation for immersed interface solutions

Ben A. Vanderlei, Matthew M. Hopkins, Lisa J. Fauci
2012 Discrete and continuous dynamical systems. Series B  
We present an error estimation method for immersed interface solutions of elliptic boundary value problems. As opposed to an asymptotic rate that indicates how the errors in the numerical method converge to zero, we seek a posteriori estimates of the errors, and their spatial distribution, for a given solution. Our estimate is based upon the classical idea of defect corrections, which requires the application of a higher-order discretization operator to a solution achieved with a lower-order
more » ... th a lower-order discretization. Our model problem will be an elliptic boundary value problem in which the coefficients are discontinuous across an internal boundary.
doi:10.3934/dcdsb.2012.17.1185 fatcat:43pq2rld6revxnrrkkkgy6y7am