On computable bounds So far, all error bounds we have shown involve the unknown solution u bounds is based on some regularity assumptions on u and on The validity of the the domain Ω These bounds are suitable to demonstrate convergence rates in the assumed solution regularity scenarios. Hence the name a priori (meaning from the start/with given in this context) Key Question Is it possible to derive computable error bounds, e.g. of the form for various norms? Key idea: Use residuals For instance, let Ax b AE Rnxn invertible, x, b e R" linear system. An approximation xo of the exact solution x, satisfies the bound On computable bounds So far, all error bounds we have shown involve the unknown solution u bounds is based on some regularity assumptions on u and on The validity of the the domain Ω These bounds are suitable to demonstrate convergence rates in the assumed solution regularity scenarios. Hence the name a priori (meaning from the start/with given in this context) Key Question Is it possible to derive computable error bounds, e.g. of the form for various norms? Key idea: Use residuals For instance, let Ax b AE Rnxn invertible, x, b e R" linear system. An approximation xo of the exact solution x, satisfies the bound