For the Hodge–Laplace equation in finite element exterior calculus, we introduce several
families of discontinuous Galerkin methods in the extended Galerkin framework. For …

Due to the indefiniteness and poor spectral properties, the discretized linear algebraic
system of the vector Laplacian by mixed finite element methods is hard to solve. A block …

Finite element approximation to a decoupled formulation for the quad-curl problem is
studied in this paper. The difficulty of constructing elements with certain conformity to the …

In this paper, we present several new a posteriori error estimators and two adaptive mixed
finite element methods AMFEM1 and AMFEM2 for the Hodge Laplacian problem in finite …

Optimal order error estimates of the energy-preserving numerical methods for solving the
Hodge wave equation is obtained in this paper. Based on the de Rham complex, the Hodge …

We present residual-based a posteriori error estimates of mixed finite element methods for
the three-field formulation of Biot's consolidation model. The error estimator are upper and …

For a generalized Hodge Laplace equation, we prove the quasi-optimal convergence rate of
an adaptive mixed finite element method. This adaptive method can control the error in the …

It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can
be used to solve the Helmholtz equation in unbounded domains. In this work, applying such …

We introduce and explain key relations between a posteriori error estimates and subspace
correction methods viewed as preconditioners for problems in infinite dimensional Hilbert …

Finite Element Exterior Calculus (FEEC) was developed by Arnold, Falk, Winther and others
over the last decade to exploit the observation that mixed variational problems can be posed …