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03/24/2023
Two Finite Element Approaches For The Porous Medium Equation That Are Positivity Preserving And Energy Stable
In this work, we present the construction of two distinct finite element...
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03/12/2023
hp-Multigrid preconditioner for a divergence-conforming HDG scheme for the incompressible flow problems
In this study, we present an hp-multigrid preconditioner for a divergenc...
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02/27/2023
High-order variational Lagrangian schemes for compressible fluids
We present high-order variational Lagrangian finite element methods for ...
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09/12/2022
A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous media
We present a novel hybridizable discontinuous Galerkin (HDG) method on u...
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08/30/2022
Optimal geometric multigrid preconditioners for HDG-P0 schemes for the reaction-diffusion equation and the generalized Stokes equations
We present the lowest-order hybridizable discontinuous Galerkin schemes ...
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01/31/2022
A high-order velocity-based discontinuous Galerkin scheme for the shallow water equations: local conservation, entropy stability, well-balanced property, and positivity preserv
We present a novel class of locally conservative, entropy stable and wel...
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11/13/2021
A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media
We present a hybrid-mixed finite element method for a novel hybrid-dim...
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05/03/2021
High-order space-time finite element methods for the Poisson-Nernst-Planck equations: Positivity and unconditional energy stability
We present a novel class of high-order space-time finite element schemes...
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04/28/2021
Uniform block diagonal preconditioners for divergence-conforming HDG Methods for the generalized Stokes problem and linear elasticity
We propose a uniform block diagonal preconditioner for the condensed H(d...
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03/28/2021
Arbitrary Lagrangian-Eulerian hybridizable discontinuous Galerkin methods for fluid-structure interaction
We present a novel (high-order) hybridizable discontinuous Galerkin (HDG...
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03/15/2021
A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations
The basis generation in reduced order modeling usually requires multiple...
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11/30/2020
A monolithic divergence-conforming HDG scheme for a linear fluid-structure interaction model
We present a novel monolithic divergence-conforming HDG scheme for a lin...
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11/24/2020
Uniform auxiliary space preconditioning for HDG methods for elliptic operators with a parameter dependent low order term
The auxiliary space preconditioning (ASP) technique is applied to the HD...
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04/17/2020
POD-(H)DG Method for Incompressible Flow Simulations
We present a reduced order method (ROM) based on proper orthogonal decom...
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02/21/2020
A divergence-free HDG scheme for the Cahn-Hilliard phase-field model for two-phase incompressible flow
We construct a divergence-free HDG scheme for the Cahn-Hilliard-Navier-S...
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01/23/2020
Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity
Robust discretization methods for (nearly-incompressible) linear elastic...
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12/16/2019