Computable estimates of the distance to the exact solution of the evolutionary reaction-diffusion equation
Provides guaranteed error estimates for numerical solutions of reaction-diffusion PDEs, which is important for reliability in scientific computing.
The paper derives computable two-sided error bounds for the evolutionary reaction-diffusion equation with mixed boundary conditions, and numerical experiments confirm the bounds are accurate and efficient for local error indication.
We derive guaranteed bounds of distance to the exact solution of the evolutionary reaction-diffusion problem with mixed Dirichlet-Neumann boundary condition. It is shown that two-sided error estimates are directly computable and equivalent to the error. Numerical experiments confirm that estimates provide accurate two-sided bounds of the overall error and generate efficient indicators of local error distribution.