A posteriori error estimates for a coupled piezoelectric model

Abstract The paper addresses a coupled problem describing piezoelectric effects in an elastic body. In this context, we derive upper bounds for the distance between the exact solution and any approximation within the corresponding energy class of functions that satisfy the boundary conditions. These upper bounds are fully computable and do not involve mesh‐dependent constants. They vanish if and only if an approximate solution exactly matches the exact one, offering a practical measure of accuracy based on the natural energy norm associated with the studied coupled problem.