Abstract
In this note we consider a parabolic evolution equation in a polygonal space-time cylinder. We show, that the elliptic part is given by a m-accretive mapping from Lq(Ω) → Lq(Ω). Therefore we can apply the theory of nonlinear semigroups in Banach spaces in order to get regularity results in time and space.
The second part of the paper deals with the numerical solution of the problem. It is dedicated to the application of the space-time discontinuous Galerkin method (STDGM). It means that both in space as well as in time discontinuous piecewise polynomial approximations of the solution are used. We concentrate to the theoretical analysis of the error estimation.
Funding statement: The research of M. Balázsová was supported by the Ministry of Education, Youth and Sports of the Czech Republic under the OP RDE grant No. CZ.02.1.01/0.0/0.0/16 019/0000778/Centre for Advanced Applied Sciences, group THEORY. The research of M. Feistauer was supported by the grant No. 20-01074 of the Czech Science Foundation.
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