Matches in SemOpenAlex for { <https://semopenalex.org/work/W4313443958> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W4313443958 abstract "We present a new perspective on the use of weighted essentially nonoscillatory (WENO) reconstructions in high-order methods for scalar hyperbolic conservation laws. The main focus of this work is on nonlinear stabilization of continuous Galerkin (CG) approximations. The proposed methodology also provides an interesting alternative to WENO-based limiters for discontinuous Galerkin (DG) methods. Unlike Runge--Kutta DG schemes that overwrite finite element solutions with WENO reconstructions, our approach uses a reconstruction-based smoothness sensor to blend the numerical viscosity operators of high- and low-order stabilization terms. The so-defined WENO approximation introduces low-order nonlinear diffusion in the vicinity of shocks, while preserving the high-order accuracy of a linearly stable baseline discretization in regions where the exact solution is sufficiently smooth. The underlying reconstruction procedure performs Hermite interpolation on stencils consisting of a mesh cell and its neighbors. The amount of numerical dissipation depends on the relative differences between partial derivatives of reconstructed candidate polynomials and those of the underlying finite element approximation. All derivatives are taken into account by the employed smoothness sensor. To assess the accuracy of our CG-WENO scheme, we derive error estimates and perform numerical experiments. In particular, we prove that the consistency error of the nonlinear stabilization is of the order $p+1/2$, where $p$ is the polynomial degree. This estimate is optimal for general meshes. For uniform meshes and smooth exact solutions, the experimentally observed rate of convergence is as high as $p+1$." @default.
- W4313443958 created "2023-01-06" @default.
- W4313443958 creator A5040405945 @default.
- W4313443958 creator A5090390734 @default.
- W4313443958 date "2022-12-29" @default.
- W4313443958 modified "2023-09-26" @default.
- W4313443958 title "Dissipation-based WENO stabilization of high-order finite element methods for scalar conservation laws" @default.
- W4313443958 doi "https://doi.org/10.48550/arxiv.2212.14224" @default.
- W4313443958 hasPublicationYear "2022" @default.
- W4313443958 type Work @default.
- W4313443958 citedByCount "0" @default.
- W4313443958 crossrefType "posted-content" @default.
- W4313443958 hasAuthorship W4313443958A5040405945 @default.
- W4313443958 hasAuthorship W4313443958A5090390734 @default.
- W4313443958 hasBestOaLocation W43134439581 @default.
- W4313443958 hasConcept C102634674 @default.
- W4313443958 hasConcept C121332964 @default.
- W4313443958 hasConcept C134306372 @default.
- W4313443958 hasConcept C135402231 @default.
- W4313443958 hasConcept C135628077 @default.
- W4313443958 hasConcept C158622935 @default.
- W4313443958 hasConcept C176321772 @default.
- W4313443958 hasConcept C2524010 @default.
- W4313443958 hasConcept C28826006 @default.
- W4313443958 hasConcept C31487907 @default.
- W4313443958 hasConcept C33923547 @default.
- W4313443958 hasConcept C3445786 @default.
- W4313443958 hasConcept C39177556 @default.
- W4313443958 hasConcept C48753275 @default.
- W4313443958 hasConcept C57691317 @default.
- W4313443958 hasConcept C62520636 @default.
- W4313443958 hasConcept C73000952 @default.
- W4313443958 hasConcept C92244383 @default.
- W4313443958 hasConcept C97355855 @default.
- W4313443958 hasConceptScore W4313443958C102634674 @default.
- W4313443958 hasConceptScore W4313443958C121332964 @default.
- W4313443958 hasConceptScore W4313443958C134306372 @default.
- W4313443958 hasConceptScore W4313443958C135402231 @default.
- W4313443958 hasConceptScore W4313443958C135628077 @default.
- W4313443958 hasConceptScore W4313443958C158622935 @default.
- W4313443958 hasConceptScore W4313443958C176321772 @default.
- W4313443958 hasConceptScore W4313443958C2524010 @default.
- W4313443958 hasConceptScore W4313443958C28826006 @default.
- W4313443958 hasConceptScore W4313443958C31487907 @default.
- W4313443958 hasConceptScore W4313443958C33923547 @default.
- W4313443958 hasConceptScore W4313443958C3445786 @default.
- W4313443958 hasConceptScore W4313443958C39177556 @default.
- W4313443958 hasConceptScore W4313443958C48753275 @default.
- W4313443958 hasConceptScore W4313443958C57691317 @default.
- W4313443958 hasConceptScore W4313443958C62520636 @default.
- W4313443958 hasConceptScore W4313443958C73000952 @default.
- W4313443958 hasConceptScore W4313443958C92244383 @default.
- W4313443958 hasConceptScore W4313443958C97355855 @default.
- W4313443958 hasLocation W43134439581 @default.
- W4313443958 hasOpenAccess W4313443958 @default.
- W4313443958 hasPrimaryLocation W43134439581 @default.
- W4313443958 hasRelatedWork W2000845182 @default.
- W4313443958 hasRelatedWork W2037880619 @default.
- W4313443958 hasRelatedWork W2120889345 @default.
- W4313443958 hasRelatedWork W2142212336 @default.
- W4313443958 hasRelatedWork W2380080472 @default.
- W4313443958 hasRelatedWork W2733331010 @default.
- W4313443958 hasRelatedWork W2965585506 @default.
- W4313443958 hasRelatedWork W3007482804 @default.
- W4313443958 hasRelatedWork W3090384263 @default.
- W4313443958 hasRelatedWork W4287866116 @default.
- W4313443958 isParatext "false" @default.
- W4313443958 isRetracted "false" @default.
- W4313443958 workType "article" @default.