The authors present a non-overlapping domain decomposition methodfor reaction diffusion problems. An a posteriori error estimate isderived, bounding the error on subdomains by using differences of tracesof the subdomain solutions. The method is implemented numerically usinga finite element discretization of the domain decomposition algorithm,and a numerical example is provided.

Using a combination of domain decomposition and finite elementmethods, a posteriori error estimates for a problem of reactiondiffusion with exact solution are derived. The numerical problem issolved using domain decomposition with four subdomains and withdifferent triangulations.

Interface conditions of the Robin type are used. An originaltheorem shows how the a posteriori error estimate depends on theiterative domain decomposition and on the finite element discretization.The first term of the a posteriori error estimate depends on a termmeasuring discontinuity of the domain decomposition solution across theinterface &Ggr;.