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 language | English |
|---|---|
| Pages (from-to) | A2543-A2567 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 40 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2018 Jan 1 |
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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 journal › Article
TY - JOUR
T1 - A staggered discontinuous Galerkin method of minimal dimension on quadrilateral and polygonal meshes
AU - Zhao, Lina
AU - Park, Eun Jae
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85053760828&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85053760828&partnerID=8YFLogxK
U2 - 10.1137/17M1159385
DO - 10.1137/17M1159385
M3 - Article
AN - SCOPUS:85053760828
VL - 40
SP - A2543-A2567
JO - SIAM Journal of Scientific Computing
JF - SIAM Journal of Scientific Computing
SN - 1064-8275
IS - 4
ER -