# Discontinuous Galerkin method for an elliptic problem with nonlinear Newton boundary conditions in a polygon

@article{Feistauer2019DiscontinuousGM, title={Discontinuous Galerkin method for an elliptic problem with nonlinear Newton boundary conditions in a polygon}, author={Miloslav Feistauer and Filip Roskovec and Anna‐Margarete S{\"a}ndig}, journal={Ima Journal of Numerical Analysis}, year={2019}, volume={39}, pages={423-453} }

The paper is concerned with the analysis of the discontinuous Galerkin method (DGM) for the numerical solution of an elliptic boundary value problem with a nonlinear Newton boundary condition in a two-dimensional polygonal domain. Using the monotone operator theory it is possible to prove the existence and uniqueness of the exact weak solution and the approximate DG solution. The main attention is paid to the study of error estimates. To this end, the regularity of the weak solution is…

## 5 Citations

### Analysis of the FEM and DGM for an elliptic problem with a nonlinear Newton boundary condition

- Mathematics
- 2017

The paper is concerned with the numerical analysis of an elliptic equation in a polygon with a nonlinear Newton boundary condition, discretized by the finite element or discontinuous Galerkin…

### Regularity results and numerical solution by the discontinuous Galerkin method to semilinear parabolic initial boundary value problems with nonlinear Newton boundary conditions in a polygonal space-time cylinder

- MathematicsJournal of Numerical Mathematics
- 2022

Abstract In this note we consider a parabolic evolution equation in a polygonal space-time cylinder. We show, that the elliptic part is given by a m-accretive mapping from Lq(Ω) → Lq(Ω). Therefore we…

### A discontinuous Galerkin scheme for a large class of elliptic equations

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- 2021

A discontinuous Galerkin internal-penalty scheme that is applicable to a large class of linear and non-linear elliptic partial differential equations and the foundation of the elliptic solver for the SpECTRE numerical relativity code is presented.

### Regularity results to semilinear Parabolic Initial Boundary Value Problems with Nonlinear Newton Boundary Conditions in a polygonal space-time cylinder

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- 2020

In this paper some semilinear parabolic problems with nonlinear Newton boundary conditions in a polygonal space-time cylinder are considered: a simple model problem, see [7], more advanced problems…

### Unified discontinuous Galerkin scheme for a large class of elliptic equations

- MathematicsPhysical Review D
- 2022

A discontinuous Galerkin internal-penalty scheme that is applicable to a large class of linear and nonlinear elliptic partial differential equations, and implemented in the open-source SpECTRE numerical relativity code.

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