A staggered discontinuous Galerkin method of minimal dimension on quadrilateral and polygonal meshes

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Original languageEnglish
Pages (from-to)A2543-A2567
Journal / PublicationSIAM Journal on Scientific Computing
Issue number4
Publication statusPublished - 2018
Externally publishedYes


In this paper, we first propose and analyze a locally conservative, lowest order staggered discontinuous Galerkin method of minimal dimension on general quadrilateral/polygonal meshes for elliptic problems. The method can be flexibly applied to rough grids such as the highly distorted trapezoidal grid, and both h perturbation and h2 perturbation of the smooth grids. Optimal convergence rates for both the potential and vector variables are achieved for smooth solutions. On the other hand, the lowest order method can be particularly useful for computing rough solutions. We provide a priori error analysis for problems with low regularity. Next, adaptive mesh refinement is an attractive tool for general meshes due to their flexibility and simplicity in handling hanging nodes. Therefore, we derive a simple residual-type error estimator on the L2 error in vector variable, and the reliability and efficiency of the proposed error estimator are proved. Numerical results indicate that optimal convergence can be achieved for both the potential and vector variables, and the singularity can be well-captured by the proposed error estimator.

Research Area(s)

  • A posteriori error estimation, DG method, Low regularity, Lowest order method, Minimal dimension, Quadrilateral/polygonal meshes, Staggered grid

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