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We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction-diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite…
A virtual element discretisation of an Arbitrary Lagrangian-Eulerian method for two-dimensional convection-diffusion equations is proposed employing an isoparametric Virtual Element Method to achieve higher-order convergence rates on curved…
This paper studies adaptive least-squares finite element methods for convection-dominated diffusion-reaction problems. The least-squares methods are based on the first-order system of the primal and dual variables with various ways of…
The Reynolds equation, combined with the Elrod algorithm for including the effect of cavitation, resembles a nonlinear convection-diffusion-reaction (CDR) equation. Its solution by finite elements is prone to oscillations in…
This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Rigorous numerical analysis for this…
This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the…
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…
In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
First we introduce and analyze a convergent numerical method for a large class of nonlinear nonlocal possibly degenerate convection diffusion equations. Secondly we develop a new Kuznetsov type theory and obtain general and possibly optimal…
We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…
Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite element method in the spirit of the Localized Orthogonal…
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…
This article devises a new primal-dual weak Galerkin finite element method for the convection-diffusion equation. Optimal order error estimates are established for the primal-dual weak Galerkin approximations in various discrete norms and…
We present here a new stochastic modelling in the constitution of fluid flow reduced-order models. This framework introduces a spatially inhomogeneous random field to represent the unresolved small-scale velocity component. Such a…