A WEAK GALERKIN METHOD FOR SECOND ORDER ELLIPTIC PROBLEMS WITH POLYNOMIAL REDUCTION

Nolisa Malluwawadu; Saqib Hussain

doi:10.11948/2156-907X.20180137

2019 Volume 9 Issue 2

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Nolisa Malluwawadu, Saqib Hussain. A WEAK GALERKIN METHOD FOR SECOND ORDER ELLIPTIC PROBLEMS WITH POLYNOMIAL REDUCTION[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 655-670. doi: 10.11948/2156-907X.20180137

Citation:

Nolisa Malluwawadu, Saqib Hussain. A WEAK GALERKIN METHOD FOR SECOND ORDER ELLIPTIC PROBLEMS WITH POLYNOMIAL REDUCTION[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 655-670. doi: 10.11948/2156-907X.20180137

A WEAK GALERKIN METHOD FOR SECOND ORDER ELLIPTIC PROBLEMS WITH POLYNOMIAL REDUCTION

Nolisa Malluwawadu^1, ,,
Saqib Hussain²

1.
Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA
2.
Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

Corresponding author: Email address: nolisa.malluwawadu@colostate.edu (N. Malluwawadu)

Abstract

Abstract

The second order elliptic equation, which is also know as the diffusion-convection equation, is of great interest in many branches of physics and industry. In this paper, we use the weak Galerkin finite element method to study the general second order elliptic equation. A weak Galerkin finite element method is proposed and analyzed. This scheme features piecewise polynomials of degree $k\geq 1$ on each element and piecewise polynomials of degree $k-1\geq 0$ on each edge or face of the element. Error estimates of optimal order of convergence rate are established in both discrete $H^1$ and standard $L^2$ norm. The paper also presents some numerical experiments to verify the efficiency of the method.
- Galerkin finite element methods /
- second-order elliptic problems /
- discrete gradient /
- mixed finite element methods
MSC: 65N15, 65N30, 35J50

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References

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