Erratum. On the Multi-Level Splitting of Finite Element Spaces.(Numer. Math. 49, 379-412 (1986)).
The phase relaxation model is a diffuse interface model with small parameter ε which consists of a parabolic PDE for temperature θ and an ODE with double obstacles for phase variable χ. To decouple the system a semi-explicit Euler method with variable step-size τ is used for time discretization, which requires the stability constraint τ ≤ ε. Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter h are further employed for space discretization. A posteriori...
We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.
For convection-diffusion problems with exponential layers, optimal error estimates for linear finite elements on Shishkin-type meshes are known. We present the first optimal convergence result in an energy norm for a Bakhvalov-type mesh.