Error estimation for immersed interface solutions
Ben Vanderlei, Matthew Hopkins, Lisa Fauci · Discrete and Continuous Dynamical Systems - B · 2012
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 seeka 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 operatorto a solution achieved with a lower-order discretization.Our model problem will be an elliptic boundary valueproblem in which the coefficients are discontinuous across an internal boundary.