Unconditionally optimal \(H^1\)-norm error estimates of a fast and linearized Galerkin method for nonlinear subdiffusion equations
The authors consider a semi-linear subdiffusion equation. They first consider a discretization in time given by a set of some special mesh points and derived a convenient semi-discrete scheme (discretization only in time). This semi-discrete scheme is based on a Newton linearized method. An analysis for the convergence is provided. Thanks to this semi-discrete scheme, a fully discrete scheme based on the use of the Galerkin method as discretization in space is established and a convergence analysis in \(H^1\)-norm is also given. Some numerical examples are presented to support the theoretical results.
scientific article; zbMATH DE number 7469197
scientific article