| 1. |
- Bastian, Peter, et al.
(författare)
-
Adaptive Modelling of Coupled Hydrological Processes with Application in Water Management
- 2012
-
Ingår i: Progress in Industrial Mathematics at ECMI 2010. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783642251009 ; , s. 561-567
-
Konferensbidrag (refereegranskat)abstract
- This paper presents recent results of a network project aiming at the modelling and simulation of coupled surface and subsurface flows. In particular, a discontinuous Galerkin method for the shallow water equations has been developed which includes a special treatment of wetting and drying. A robust solver for saturated–unsaturated groundwater flow in homogeneous soil is at hand, which, by domain decomposition techniques, can be reused as a subdomain solver for flow in heterogeneous soil. Coupling of surface and subsurface processes is implemented based on a heterogeneous nonlinear Dirichlet–Neumann method, using the dune-grid-glue module in the numerics software DUNE.
|
|
| 2. |
- Dedner, Andreas, et al.
(författare)
-
Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Methods
- 2022
-
Ingår i: Communications on Applied Mathematics and Computation. - : Springer Science and Business Media LLC. - 2096-6385 .- 2661-8893. ; 4:2, s. 657-696
-
Tidskriftsartikel (refereegranskat)abstract
- This paper discusses a Python interface for the recently published Dune-Fem-DG module which provides highly efficient implementations of the discontinuous Galerkin (DG) method for solving a wide range of nonlinear partial differential equations (PDEs). Although the C++ interfaces of Dune-Fem-DG are highly flexible and customizable, a solid knowledge of C++ is necessary to make use of this powerful tool. With this work, easier user interfaces based on Python and the unified form language are provided to open Dune-Fem-DG for a broader audience. The Python interfaces are demonstrated for both parabolic and first-order hyperbolic PDEs.
|
|
| 3. |
- Dedner, Andreas, et al.
(författare)
-
Residual Estimates for Post-processors in Elliptic Problems
- 2021
-
Ingår i: Journal of Scientific Computing. - : Springer Nature. - 0885-7474 .- 1573-7691. ; 88:2
-
Tidskriftsartikel (refereegranskat)abstract
- In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that “tweaks” a wide variety of existing post-processing techniques to enable efficient and reliable a posteriori bounds to be proven. This ultimately results in optimal error control for all manner of reconstruction operators, including those that superconverge. We showcase our results by applying them to two classes of very popular reconstruction operators, the Smoothness-Increasing Accuracy-Conserving filter and superconvergent patch recovery. Extensive numerical tests are conducted that confirm our analytic findings.
|
|
