Abstract
In this paper we derive regularity results for equilibria of multilattices under an
external force and prove a priori and a posteriori error estimates for a multiscale numerical method forcomputing such equilibria. The estimates are derived in a W1,8 norm in one space dimension. One of the features of our analysis is that we establish an equivalent way of formulating the coarse-grained problem which greatly simplifies derivation of the error bounds (both a priori and a posteriori). We
illustrate our error estimates with numerical experiments.
external force and prove a priori and a posteriori error estimates for a multiscale numerical method forcomputing such equilibria. The estimates are derived in a W1,8 norm in one space dimension. One of the features of our analysis is that we establish an equivalent way of formulating the coarse-grained problem which greatly simplifies derivation of the error bounds (both a priori and a posteriori). We
illustrate our error estimates with numerical experiments.
| Original language | English |
|---|---|
| Pages (from-to) | 2357-2379 |
| Number of pages | 23 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 51 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2013 |