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08/18/2022
A posteriori error estimates for discontinuous Galerkin methods on polygonal and polyhedral meshes
We present a new residual-type energy-norm a posteriori error analysis f...
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06/01/2022
Discrete Gradient Flow Approximations of High Dimensional Evolution Partial Differential Equations via Deep Neural Networks
We consider the approximation of initial/boundary value problems involvi...
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08/05/2021
Robust interior penalty discontinuous Galerkin methods
Classical interior penalty discontinuous Galerkin (IPDG) methods for dif...
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07/09/2020
GPU-accelerated discontinuous Galerkin methods on polytopic meshes
Discontinuous Galerkin (dG) methods on meshes consisting of polygonal/po...
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05/12/2020
Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods
We present a posteriori error estimates for inconsistent and non-hierarc...
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09/27/2019
Convergence of adaptive discontinuous Galerkin methods (corrected version of [Math. Comp. 87 (2018), no. 314, 2611–2640])
We develop a general convergence theory for adaptive discontinuous Galer...
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07/29/2019