69 citations · 79 across the 11 of their papers we have counts for
3 papers · 1 filter
On some linear parabolic PDEs on moving hypersurfaces
Amal Alphonse, Charles M. Elliott, Björn Stinner
We consider existence and uniqueness for several examples of linear parabolic equations formulated on moving hypersurfaces. Specifically, we study in turn a surface heat equation,…
An abstract framework for parabolic PDEs on evolving spaces
Amal Alphonse, Charles M. Elliott, Björn Stinner
We present an abstract framework for treating the theory of well-posedness of solutions to abstract parabolic partial differential equations on evolving Hilbert spaces. This theory…
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…