A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations

A PDE approach to fractional diffusion: A posteriori error analysis

We derive a computable a posteriori error estimator for the αharmonic extension problem, which localizes the fractional powers of elliptic operators supplemented with Dirichlet boundary conditions. Our a posteriori error estimator relies on the solution of small discrete problems on anisotropic cylindrical stars. It exhibits built-in flux equilibration and is equivalent to the energy error up t...

Finite Element Method for Linear Multiterm Fractional Differential Equations

Numerical Algorithms for Time - Fractional Subdiffusion

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with...

A posteriori error indicators for Maxwell’s Equations

In this paper we shall analyze a class of a posteriori error indicators for an electromagnetic scattering problem for Maxwell’s equations in the presence of a bounded, inhomogeneous and anisotropic scatterer. Problems of this type arise when computing the interaction of electromagnetic radiation with biological tissue. We brie y recall existence and uniqueness theory associated with this proble...

A posteriori error estimates for Maxwell equations

Maxwell equations are posed as variational boundary value problems in the function space H(curl) and are discretized by Nédélec finite elements. In Beck et al., 2000, a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain. In the present paper, we prove the reliability of that error estimator on Lipschitz domains. The key is to establish ...