Regularity results and numerical solution by the discontinuous Galerkin method to semilinear parabolic initial boundary value problems with nonlinear Newton boundary conditions in a polygonal space-time cylinder
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Monika Balázsová
,
Miloslav Feistauer
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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© 2023 Walter de Gruyter GmbH, Berlin/ Boston, Germany
Artikel in diesem Heft
- Frontmatter
- Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
- Regularity results and numerical solution by the discontinuous Galerkin method to semilinear parabolic initial boundary value problems with nonlinear Newton boundary conditions in a polygonal space-time cylinder
- How to prove optimal convergence rates for adaptive least-squares finite element methods
- Loosely coupled, non-iterative time-splitting scheme based on Robin–Robin coupling: Unified analysis for parabolic/parabolic and parabolic/hyperbolic problems
Artikel in diesem Heft
- Frontmatter
- Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
- Regularity results and numerical solution by the discontinuous Galerkin method to semilinear parabolic initial boundary value problems with nonlinear Newton boundary conditions in a polygonal space-time cylinder
- How to prove optimal convergence rates for adaptive least-squares finite element methods
- Loosely coupled, non-iterative time-splitting scheme based on Robin–Robin coupling: Unified analysis for parabolic/parabolic and parabolic/hyperbolic problems
