Zobrazeno 1 - 10
of 215
pro vyhledávání: '"Georgoulis, Emmanuil"'
We introduce a new level-set shape optimization approach based on polytopic (i.e., polygonal in two and polyhedral in three spatial dimensions) discontinuous Galerkin methods. The approach benefits from the geometric mesh flexibility of polytopic dis
Externí odkaz:
http://arxiv.org/abs/2408.13206
We propose a new stabilised finite element method for the classical Kolmogorov equation. The latter serves as a basic model problem for large classes of kinetic-type equations and, crucially, is characterised by degenerate diffusion. The stabilisatio
Externí odkaz:
http://arxiv.org/abs/2401.12921
We develop a novel deep learning approach for pricing European basket options written on assets that follow jump-diffusion dynamics. The option pricing problem is formulated as a partial integro-differential equation, which is approximated via a new
Externí odkaz:
http://arxiv.org/abs/2401.06740
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones and seeks th
Externí odkaz:
http://arxiv.org/abs/2304.01067
We present a new residual-type energy-norm a posteriori error analysis for interior penalty discontinuous Galerkin (dG) methods for linear elliptic problems. The new error bounds are also applicable to dG methods on meshes consisting of elements with
Externí odkaz:
http://arxiv.org/abs/2208.08685
We consider the approximation of initial/boundary value problems involving, possibly high-dimensional, dissipative evolution partial differential equations (PDEs) using a deep neural network framework. More specifically, we first propose discrete gra
Externí odkaz:
http://arxiv.org/abs/2206.00290
Autor:
Dong, Zhaonan, Georgoulis, Emmanuil H.
Classical interior penalty discontinuous Galerkin (IPDG) methods for diffusion problems require a number of assumptions on the local variation of mesh-size, polynomial degree, and of the diffusion coefficient to determine the values of the, so-called
Externí odkaz:
http://arxiv.org/abs/2108.02642
Discontinuous Galerkin (dG) methods on meshes consisting of polygonal/polyhedral (henceforth, collectively termed as \emph{polytopic}) elements have received considerable attention in recent years. Due to the physical frame basis functions used typic
Externí odkaz:
http://arxiv.org/abs/2007.04881
We present a posteriori error estimates for inconsistent and non-hierarchical Galerkin methods for linear parabolic problems, allowing them to be used in conjunction with very general mesh modification for the first time. We treat schemes which are n
Externí odkaz:
http://arxiv.org/abs/2005.05661
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