60 citations · 361 across the 27 of their papers we have counts for
4 papers · 1 filter
Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems
Alexandre Ern, Iain Smears, Martin Vohralík
We consider the a posteriori error analysis of approximations of parabolic problems based on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily high…
Discrete -robust -liftings and a posteriori estimates for elliptic problems with source terms
Alexandre Ern, Iain Smears, Martin Vohralík
We establish the existence of liftings into discrete subspaces of of piecewise polynomial data on locally refined simplicial partitions of polygonal/poly…
Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method
Iain Smears
The discontinuous Galerkin time-stepping method has many advantageous properties for solving parabolic equations. However, it requires the solution of a large nonsymmetric system a…
Stable discontinuous Galerkin FEM without penalty parameters
Lorenz John, Michael Neilan, Iain Smears
We propose a modified local discontinuous Galerkin (LDG) method for second--order elliptic problems that does not require extrinsic penalization to ensure stability. Stability is i…