Matches in SemOpenAlex for { <https://semopenalex.org/work/W4308505711> ?p ?o ?g. }
Showing items 1 to 60 of
60
with 100 items per page.
- W4308505711 abstract "We consider space-time tracking type distributed optimal control problems for the wave equation in the space-time domain $Q:= Omega times (0,T) subset {mathbb{R}}^{n+1}$, where the control is assumed to be in the energy space $[H_{0;,0}^{1,1}(Q)]^*$, rather than in $L^2(Q)$ which is more common. While the latter ensures a unique state in the Sobolev space $H^{1,1}_{0;0,}(Q)$, this does not define a solution isomorphism. Hence we use an appropriate state space $X$ such that the wave operator becomes an isomorphism from $X$ onto $[H_{0;,0}^{1,1}(Q)]^*$. Using space-time finite element spaces of piecewise linear continuous basis functions on completely unstructured but shape regular simplicial meshes, we derive a priori estimates for the error $|widetilde{u}_{varrho h}-overline{u}|_{L^2(Q)}$ between the computed space-time finite element solution $widetilde{u}_{varrho h}$ and the target function $overline{u}$ with respect to the regularization parameter $varrho$, and the space-time finite element mesh-size $h$, depending on the regularity of the desired state $overline{u}$. These estimates lead to the optimal choice $varrho=h^2$ in order to define the regularization parameter $varrho$ for a given space-time finite element mesh size $h$, or to determine the required mesh size $h$ when $varrho$ is a given constant representing the costs of the control. The theoretical results will be supported by numerical examples with targets of different regularities, including discontinuous targets. Furthermore, an adaptive space-time finite element scheme is proposed and numerically analyzed." @default.
- W4308505711 created "2022-11-12" @default.
- W4308505711 creator A5037762950 @default.
- W4308505711 creator A5046290186 @default.
- W4308505711 date "2022-11-04" @default.
- W4308505711 modified "2023-09-27" @default.
- W4308505711 title "Space-time finite element methods for distributed optimal control of the wave equation" @default.
- W4308505711 doi "https://doi.org/10.48550/arxiv.2211.02562" @default.
- W4308505711 hasPublicationYear "2022" @default.
- W4308505711 type Work @default.
- W4308505711 citedByCount "0" @default.
- W4308505711 crossrefType "posted-content" @default.
- W4308505711 hasAuthorship W4308505711A5037762950 @default.
- W4308505711 hasAuthorship W4308505711A5046290186 @default.
- W4308505711 hasBestOaLocation W43085057111 @default.
- W4308505711 hasConcept C114614502 @default.
- W4308505711 hasConcept C121332964 @default.
- W4308505711 hasConcept C134306372 @default.
- W4308505711 hasConcept C135628077 @default.
- W4308505711 hasConcept C138885662 @default.
- W4308505711 hasConcept C154945302 @default.
- W4308505711 hasConcept C164660894 @default.
- W4308505711 hasConcept C2776135515 @default.
- W4308505711 hasConcept C2778572836 @default.
- W4308505711 hasConcept C33923547 @default.
- W4308505711 hasConcept C41008148 @default.
- W4308505711 hasConcept C41895202 @default.
- W4308505711 hasConcept C97355855 @default.
- W4308505711 hasConcept C99730327 @default.
- W4308505711 hasConceptScore W4308505711C114614502 @default.
- W4308505711 hasConceptScore W4308505711C121332964 @default.
- W4308505711 hasConceptScore W4308505711C134306372 @default.
- W4308505711 hasConceptScore W4308505711C135628077 @default.
- W4308505711 hasConceptScore W4308505711C138885662 @default.
- W4308505711 hasConceptScore W4308505711C154945302 @default.
- W4308505711 hasConceptScore W4308505711C164660894 @default.
- W4308505711 hasConceptScore W4308505711C2776135515 @default.
- W4308505711 hasConceptScore W4308505711C2778572836 @default.
- W4308505711 hasConceptScore W4308505711C33923547 @default.
- W4308505711 hasConceptScore W4308505711C41008148 @default.
- W4308505711 hasConceptScore W4308505711C41895202 @default.
- W4308505711 hasConceptScore W4308505711C97355855 @default.
- W4308505711 hasConceptScore W4308505711C99730327 @default.
- W4308505711 hasLocation W43085057111 @default.
- W4308505711 hasLocation W43085057112 @default.
- W4308505711 hasOpenAccess W4308505711 @default.
- W4308505711 hasPrimaryLocation W43085057111 @default.
- W4308505711 hasRelatedWork W1535410608 @default.
- W4308505711 hasRelatedWork W1973865997 @default.
- W4308505711 hasRelatedWork W1978042415 @default.
- W4308505711 hasRelatedWork W2080111856 @default.
- W4308505711 hasRelatedWork W2094879984 @default.
- W4308505711 hasRelatedWork W2317176613 @default.
- W4308505711 hasRelatedWork W3098480452 @default.
- W4308505711 hasRelatedWork W4253570894 @default.
- W4308505711 hasRelatedWork W4382469906 @default.
- W4308505711 hasRelatedWork W2604017320 @default.
- W4308505711 isParatext "false" @default.
- W4308505711 isRetracted "false" @default.
- W4308505711 workType "article" @default.