Reinforcement learning for adaptive mesh refinement

J Yang, T Dzanic, B Petersen, J Kudo… - International …, 2023 - proceedings.mlr.press
Finite element simulations of physical systems governed by partial differential equations
(PDE) crucially depend on adaptive mesh refinement (AMR) to allocate computational …

Adapted Numerical Methods for the Poisson Equation with Boundary Data in NonConvex Domains

T Apel, S Nicaise, J Pfefferer - SIAM Journal on Numerical Analysis, 2017 - SIAM
The very weak solution of the Poisson equation with L^2 boundary data is defined by the
method of transposition. The finite element solution with regularized boundary data …

[HTML][HTML] A posteriori error control for distributed elliptic optimal control problems with control constraints discretized by hp-finite elements

L Banz, M Hintermüller, A Schröder - Computers & Mathematics with …, 2020 - Elsevier
A distributed elliptic control problem with control constraints is considered, which is
formulated as a three field problem and consists of two variational equations for the state …

[HTML][HTML] A finite element method for elliptic optimal control problem on a non-convex polygon with corner singularities

HJ Choi, W Choi, Y Koh - Computers & Mathematics with Applications, 2018 - Elsevier
In this paper, we study a finite element method overcoming corner singularities for elliptic
optimal control problem posed on a polygon. Based on a corner singularity decomposition of …

Superconvergent Graded Meshes for an Elliptic Dirichlet Control Problem

T Apel, M Mateos, J Pfefferer, A Rösch - Advanced Finite Element …, 2019 - Springer
Superconvergent discretization error estimates can be obtained when the solution is smooth
enough and the finite element meshes enjoy some structural properties. The simplest one is …

hp-finite elements for pde-constrained optimal control problems with focus on distributed control and fast solvers

K Hofer - 2016 - bonndoc.ulb.uni-bonn.de
In this thesis hp-finite element methods are applied to linear quadratic optimal control
problems subject to partial differential equations. In particular two kind of model problems …