An 𝐿𝑝-DPG Method with Application to 2D Convection-Diffusion Problems
-
Jiaqi Li
and
Leszek Demkowicz
Abstract
This article summarizes the -DPG method presented in [18], where only 1D convection-diffusion problems are solved. We apply the same computational techniques to 2D convection-diffusion problems and report additional numerical results herein. Furthermore, we propose an -DPG method with variable 𝑝 and illustrate it with numerical experiments.
Funding source: National Science Foundation
Award Identifier / Grant number: 1819101
Funding statement: J. Li and L. Demkowicz were partially supported with NSF grant No. 1819101.
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Articles in the same Issue
- Frontmatter
- On the Spectrum of an Operator Associated with Least-Squares Finite Elements for Linear Elasticity
- Anisotropic Adaptive Finite Elements for an Elliptic Problem with Strongly Varying Diffusion Coefficient
- DPG Methods for a Fourth-Order div Problem
- Stable Implementation of Adaptive IGABEM in 2D in MATLAB
- Optimal Convergence of the Newton Iterative Crank–Nicolson Finite Element Method for the Nonlinear Schrödinger Equation
- Partially Discontinuous Nodal Finite Elements for 𝐻(curl) and 𝐻(div)
- Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation
- An 𝐿𝑝-DPG Method with Application to 2D Convection-Diffusion Problems
- An Improvement on a Class of Fixed Point Iterative Methods for Solving Absolute Value Equations
- Low-Regularity Integrator for the Davey–Stewartson System: Elliptic-Elliptic Case
- The Numerical Approximation to a Stochastic Age-Structured HIV/AIDS Model with Nonlinear Incidence Rates
- Qualitative Properties of Space-Dependent SIR Models with Constant Delay and Their Numerical Solutions
- A Staggered Discontinuous Galerkin Method for Quasi-Linear Second Order Elliptic Problems of Nonmonotone Type
Articles in the same Issue
- Frontmatter
- On the Spectrum of an Operator Associated with Least-Squares Finite Elements for Linear Elasticity
- Anisotropic Adaptive Finite Elements for an Elliptic Problem with Strongly Varying Diffusion Coefficient
- DPG Methods for a Fourth-Order div Problem
- Stable Implementation of Adaptive IGABEM in 2D in MATLAB
- Optimal Convergence of the Newton Iterative Crank–Nicolson Finite Element Method for the Nonlinear Schrödinger Equation
- Partially Discontinuous Nodal Finite Elements for 𝐻(curl) and 𝐻(div)
- Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation
- An 𝐿𝑝-DPG Method with Application to 2D Convection-Diffusion Problems
- An Improvement on a Class of Fixed Point Iterative Methods for Solving Absolute Value Equations
- Low-Regularity Integrator for the Davey–Stewartson System: Elliptic-Elliptic Case
- The Numerical Approximation to a Stochastic Age-Structured HIV/AIDS Model with Nonlinear Incidence Rates
- Qualitative Properties of Space-Dependent SIR Models with Constant Delay and Their Numerical Solutions
- A Staggered Discontinuous Galerkin Method for Quasi-Linear Second Order Elliptic Problems of Nonmonotone Type
