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07/31/2023
The Mixed Virtual Element Discretization for highly-anisotropic problems: the role of the boundary degrees of freedom
In this paper, we discuss the accuracy and the robustness of the mixed V...
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04/28/2023
Orthogonal polynomial bases in the Mixed Virtual Element Method
The use of orthonormal polynomial bases has been found to be efficient i...
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02/22/2023
Improving high order VEM stability on badly-shaped convex elements
For the 2D and 3D Virtual Element Method (VEM), a new approach to improv...
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02/01/2023
A first-order stabilization-free Virtual Element Method
In this paper, we introduce a new Virtual Element Method (VEM) not requi...
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11/22/2022
Weak scalability of domain decomposition methods for discrete fracture networks
Discrete Fracture Networks (DFNs) are complex three-dimensional structur...
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11/17/2022
An optimization based 3D-1D coupling strategy for tissue perfusion and chemical transport during tumor-induced angiogenesis
A new mathematical model and numerical approach are proposed for the sim...
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08/20/2022
Mesh Quality Agglomeration algorithm for the Virtual Element Method applied to Discrete Fracture Networks
We propose a quality-based optimization strategy to reduce the total num...
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05/02/2022
Solving PDEs by Variational Physics-Informed Neural Networks: an a posteriori error analysis
We consider the discretization of elliptic boundary-value problems by va...
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03/31/2022
A data-driven approach for the closure of RANS models by the divergence of the Reynolds Stress Tensor
In the present paper a new data-driven model to close and increase accur...
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03/03/2022
A PDE-constrained optimization method for 3D-1D coupled problems with discontinuous solutions
A numerical method for coupled 3D-1D problems with discontinuous solutio...
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02/17/2022
Comparison of standard and stabilization free Virtual Elements on anisotropic elliptic problems
In this letter we compare the behaviour of standard Virtual Element Meth...
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12/21/2021
Agglomeration-based geometric multigrid schemes for the Virtual Element Method
In this paper we analyse the convergence properties of two-level, W-cycl...
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12/18/2021
A new quality preserving polygonal mesh refinement algorithm for Virtual Element Methods
Mesh adaptivity is a useful tool for efficient solution to partial diffe...
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09/05/2021
Variational Physics Informed Neural Networks: the role of quadratures and test functions
In this work we analyze how Gaussian or Newton-Cotes quadrature rules of...
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06/18/2021
Efficient partitioning and reordering of conforming virtual element discretizations for large scale Discrete Fracture Network flow parallel solvers
Discrete Fracture Network models are largely used for very large scale g...
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06/09/2021
A gradient based resolution strategy for a PDE-constrained optimization approach for 3D-1D coupled problems
Coupled 3D-1D problems arise in many practical applications, in an attem...
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03/31/2021
Lowest order stabilization free Virtual Element Method for the Poisson equation
We introduce and analyse the first order Enlarged Enhancement Virtual El...
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02/12/2021
3D-1D coupling on non conforming meshes via three-field optimization based domain decomposition
A new numerical approach is proposed for the simulation of coupled three...
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04/09/2020
An optimization approach for flow simulations in poro-fractured media with complex geometries
A new discretization approach is presented for the simulation of flow in...
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01/02/2020
Anisotropic a posteriori error estimate for the Virtual Element Method
We derive an anisotropic a posteriori error estimate for the adaptive co...
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12/20/2019
A Three-Field based optimization formulation for flow simulations in networks of fractures on non conforming meshes
A new numerical scheme is proposed for flow computation in complex discr...
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12/11/2019