Certified error bounds for uncertain elliptic equations
In many applications, partial differential equations depend on parameters which are only approximately known. Using tools from functional analysis and global optimization, methods are presented for obtaining certificates for rigorous and realistic error bounds on the solution of linear elliptic partial differential equations in arbitrary domains, either in the energy norm, or of key functionals of the solution. Uncertainty in the parameters can be taken into account, either in a worst case setting, or given limited probalistic information in terms of clouds.
linear elliptic partial differential equations
scientific article; zbMATH DE number 5295237
scientific article