On the Convergence Rates of Energy- Stable Finite-Difference Schemes
نویسندگان
چکیده
We consider initial-boundary value problems, with a kth derivative in time and a highest spatial derivative of order q, and their semi-discrete finite difference approximations. With an internal truncation error of order p ≥ 1, and a boundary error of order r ≥ 0, we prove that the convergence rate is: min(p, r + q). The assumptions needed for these results to hold are: i) The continuous problem is linear and well-posed (with a smooth solution). ii) The numerical scheme is consistent, nullspace consistent and energy stable.
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