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Existence of energy-variational solutions to hyperbolic conservation laws
We introduce the concept of energy-variational solutions for hyperbolic conservation laws. Intrinsically, these energy-variational solutions fulfill...
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Analysis and Numerical Approximation of Energy-Variational Solutions to the Ericksen–Leslie Equations
We define the concept of energy-variational solutions for the Ericksen–Leslie equations in three spatial dimensions. This solution concept is finer...
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The posteriori analysis of the spectral element discretization of the wave equation
This work focuses on discretizing a second-order linear wave equation using the implicit Euler scheme for time discretization and the spectral...
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Trefftz discontinuous Galerkin discretization for the Stokes problem
We introduce a new discretization based on a polynomial Trefftz-DG method for solving the Stokes equations. Discrete solutions of this method fulfill...
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Gauss Newton Method for Solving Variational Problems of PDEs with Neural Network Discretizaitons
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based...
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Adaptive variational discretization approximation method for parabolic optimal control problems
In this paper, we study variational discretization method for parabolic optimization problems. Firstly, we obtain some convergence and...
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Element Length Calculation for Isogeometric Discretization and Complex Geometries
Flow computations with semi-discrete and space–time (ST) methods have been relying on, as core methods, variational multiscale methods and, more...
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Higher Order Time Discretization Method for the Stochastic Stokes Equations with Multiplicative Noise
In this paper, we propose a new approach for the time-discretization of the incompressible stochastic Stokes equations with multiplicative noise. Our...
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Verifiability of the Data-Driven Variational Multiscale Reduced Order Model
In this paper, we focus on the mathematical foundations of reduced order model (ROM) closures. First, we extend the verifiability concept from large...
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Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity
In this paper, we study the concept of split monotone variational inclusion problem with multiple output sets. We propose a new relaxed inertial...
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Convex Non-convex Variational Models
An important class of computational techniques to solve inverse problems in image processing relies on a variational approach: the optimal output is...
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Discrete approximation for two-stage stochastic variational inequalities
In this paper, the discrete approximation of two-stage stochastic variational inequalities has been investigated when the second stage problem has...
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Mixed and hybrid Petrov–Galerkin finite element discretization for optimal control of the wave equation
A mixed finite element discretization of an optimal control problem for the linear wave equation with homogeneous Dirichlet boundary condition is...
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Distributionally robust stochastic variational inequalities
We propose a formulation of the distributionally robust variational inequality (DRVI) to deal with uncertainties of distributions of the involved...
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The subdifferential descent method in a nonsmooth variational problem
The paper is devoted to the classical variational problem with a nonsmooth integrand of the functional to be minimized. The integrand is supposed to...
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Discrete Hamiltonian Variational Mechanics and Hamel’s Integrators
Exact variational integrators were exposed in the context of Lagrangian mechanics in Marsden and West (
2001 ). These integrators sample the...
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Mann-Type Inertial Projection and Contraction Method for Solving Split Pseudomonotone Variational Inequality Problem with Multiple Output Sets
In this paper, we study the concept of split variational inequality problem with multiple output sets when the cost operators are pseudomonotone and...
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A modified inertial Tseng technique of Bilevel variational inequality problem with application to image processing
In this paper, we propose and study a new modified Tseng inertial iterative technique for solving Bilevel quasimonotone Variational Inequality...
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Inertial iterative method for solving generalized equilibrium, variational inequality, and fixed point problems of multivalued map**s in Banach space
We devise an iterative algorithm incorporating inertial techniques to approximate the shared solution of a generalized equilibrium problem, a fixed...
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Variational Physics Informed Neural Networks: the Role of Quadratures and Test Functions
In this work we analyze how quadrature rules of different precisions and piecewise polynomial test functions of different degrees affect the...
