55 citations · 96 across the 30 of their papers we have counts for
5 papers · 1 filter
Optimal control of elliptic PDEs on surfaces of codimension 1
C. Brett, A. S. Dedner, C. M. Elliott
We consider an elliptic optimal control problem where the objective functional contains an integral along a surface of codimension 1, also known as a hypersurface. In particular, w…
Optimal control of elliptic PDEs at points
C. Brett, A. S. Dedner, C. M. Elliott
We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term…
Efficient Multigrid Preconditioners for Atmospheric Flow Simulations at High Aspect Ratio
Andreas Dedner, Eike Hermann Müller, Robert Scheichl
Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical we…
Adaptive discontinuous Galerkin methods on surfaces
Andreas Dedner, Pravin Madhavan
We present a dual weighted residual-based a posteriori error estimate for a discontinuous Galerkin (DG) approximation of a linear second-order elliptic problem on compact smooth co…
High order discontinuous Galerkin methods on surfaces
Paola Antonietti, Andreas Dedner, Pravin Madhavan +3
We derive and analyze high order discontinuous Galerkin methods for second-order elliptic problems on implicitely defined surfaces in . This is done by carefully ad…