@Article{Fidkowski2005a,
    author      = {Fidkowski, Krzysztof J. and Oliver, Todd A. and Lu, James and Darmofal, David L.},
    title       = {p-{Multigrid} solution of high-order discontinuous {Galerkin} discretizations of the compressible {Navier}--{Stokes} equations},
    doi         = {10.1016/j.jcp.2005.01.005},
    issn        = {0021-9991},
    journal     = {Journal of Computational Physics},
    month       = {July},
    number      = {1},
    pages       = {92--113},
    url         = {http://www.sciencedirect.com/science/article/pii/S0021999105000185},
    volume      = {207},
    year        = {2005},
    abstract    = {We present a p-multigrid solution algorithm for a high-order discontinuous Galerkin finite element discretization of the compressible Navier--Stokes equations. The algorithm employs an element line Jacobi smoother in which lines of elements are formed using coupling based on a p=0 discretization of the scalar convection--diffusion equation. Fourier analysis of the two-level p-multigrid algorithm for convection--diffusion shows that element line Jacobi presents a significant improvement over element Jacobi especially for high Reynolds number flows and stretched grids. Results from inviscid and viscous test cases demonstrate optimal hp+1 order of accuracy as well as p-independent multigrid convergence rates, at least up to p=3. In addition, for the smooth problems considered, p-refinement outperforms h-refinement in terms of the time required to reach a desired high accuracy level.}
}

{"_id":{"_str":"521a81b7aa2f288d1f000a0f"},"__v":0,"authorIDs":[],"author_short":["Fidkowski, K. J.","Oliver, T. A.","Lu, J.","Darmofal, D. L."],"bibbaseid":"fidkowski-oliver-lu-darmofal-pmultigridsolutionofhighorderdiscontinuousgalerkindiscretizationsofthecompressiblenavierstokesequations-2005","bibdata":{"bibtype":"article","type":"article","author":[{"propositions":[],"lastnames":["Fidkowski"],"firstnames":["Krzysztof","J."],"suffixes":[]},{"propositions":[],"lastnames":["Oliver"],"firstnames":["Todd","A."],"suffixes":[]},{"propositions":[],"lastnames":["Lu"],"firstnames":["James"],"suffixes":[]},{"propositions":[],"lastnames":["Darmofal"],"firstnames":["David","L."],"suffixes":[]}],"title":"p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations","doi":"10.1016/j.jcp.2005.01.005","issn":"0021-9991","journal":"Journal of Computational Physics","month":"July","number":"1","pages":"92–113","url":"http://www.sciencedirect.com/science/article/pii/S0021999105000185","volume":"207","year":"2005","abstract":"We present a p-multigrid solution algorithm for a high-order discontinuous Galerkin finite element discretization of the compressible Navier–Stokes equations. The algorithm employs an element line Jacobi smoother in which lines of elements are formed using coupling based on a p=0 discretization of the scalar convection–diffusion equation. Fourier analysis of the two-level p-multigrid algorithm for convection–diffusion shows that element line Jacobi presents a significant improvement over element Jacobi especially for high Reynolds number flows and stretched grids. Results from inviscid and viscous test cases demonstrate optimal hp+1 order of accuracy as well as p-independent multigrid convergence rates, at least up to p=3. In addition, for the smooth problems considered, p-refinement outperforms h-refinement in terms of the time required to reach a desired high accuracy level.","bibtex":"@Article{Fidkowski2005a,\n author = {Fidkowski, Krzysztof J. and Oliver, Todd A. and Lu, James and Darmofal, David L.},\n title = {p-{Multigrid} solution of high-order discontinuous {Galerkin} discretizations of the compressible {Navier}--{Stokes} equations},\n doi = {10.1016/j.jcp.2005.01.005},\n issn = {0021-9991},\n journal = {Journal of Computational Physics},\n month = {July},\n number = {1},\n pages = {92--113},\n url = {http://www.sciencedirect.com/science/article/pii/S0021999105000185},\n volume = {207},\n year = {2005},\n abstract = {We present a p-multigrid solution algorithm for a high-order discontinuous Galerkin finite element discretization of the compressible Navier--Stokes equations. The algorithm employs an element line Jacobi smoother in which lines of elements are formed using coupling based on a p=0 discretization of the scalar convection--diffusion equation. Fourier analysis of the two-level p-multigrid algorithm for convection--diffusion shows that element line Jacobi presents a significant improvement over element Jacobi especially for high Reynolds number flows and stretched grids. Results from inviscid and viscous test cases demonstrate optimal hp+1 order of accuracy as well as p-independent multigrid convergence rates, at least up to p=3. In addition, for the smooth problems considered, p-refinement outperforms h-refinement in terms of the time required to reach a desired high accuracy level.}\n}\n\n","author_short":["Fidkowski, K. J.","Oliver, T. A.","Lu, J.","Darmofal, D. L."],"key":"Fidkowski2005a","id":"Fidkowski2005a","bibbaseid":"fidkowski-oliver-lu-darmofal-pmultigridsolutionofhighorderdiscontinuousgalerkindiscretizationsofthecompressiblenavierstokesequations-2005","role":"author","urls":{"Paper":"http://www.sciencedirect.com/science/article/pii/S0021999105000185"},"metadata":{"authorlinks":{}},"downloads":0,"html":""},"bibtype":"article","biburl":"https://raw.githubusercontent.com/mdolab/bib-file/refs/heads/master/mdolab.bib","downloads":0,"title":"p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations","title_words":["multigrid","solution","high","order","discontinuous","galerkin","discretizations","compressible","navier","stokes","equations"],"year":2005,"dataSources":["tfb5cjQDQTFwB6ZfC","qAPjQpsx8e9aJNrSa"],"keywords":[],"search_terms":["multigrid","solution","high","order","discontinuous","galerkin","discretizations","compressible","navier","stokes","equations","fidkowski","oliver","lu","darmofal"]}