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

Lina Zhao, Eun Jae Park

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)A2543-A2567
JournalSIAM Journal on Scientific Computing
Volume40
Issue number4
DOIs
Publication statusPublished - 2018 Jan 1

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Error Estimator
Discontinuous Galerkin Method
Galerkin methods
Mesh
Grid
Rough
Lowest
Perturbation
Optimal Convergence Rate
Adaptive Mesh Refinement
Smooth Solution
Error Analysis
Elliptic Problems
Simplicity
Regularity
Flexibility
Singularity
Error analysis
Numerical Results
Computing

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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A staggered discontinuous Galerkin method of minimal dimension on quadrilateral and polygonal meshes. / Zhao, Lina; Park, Eun Jae.

In: SIAM Journal on Scientific Computing, Vol. 40, No. 4, 01.01.2018, p. A2543-A2567.

Research output: Contribution to journalArticle

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