In this work, we develop an improved shock-capturing and high-resolution Lagrangian–
Eulerian method for hyperbolic systems and balance laws. This is a new method to deal with …

In this work, we construct and analyze a new fully discrete Lagrangian-Eulerian numerical
method for the treatment of dynamics of conservation laws with nonlocal flux and influence …

In this paper, we discuss a general framework for multicontinuum homogenization.
Multicontinuum models are widely used in many applications and some derivations for these …

In this work, we design a new class of fully discrete Lagrangian–Eulerian schemes on
triangular grids to approximate nonlinear multidimensional initial value problems for scalar …

We consider linear and semilinear parabolic problems posed in high-contrast multiscale
media in two dimensions. The presence of high-contrast multiscale media adversely affects …

In this work, we introduce a new semi-discrete scheme based on the so-called no-flow
curves and its numerical analysis for solving initial value problems that involve one …

In this work, we study Riemann problems and delta-shock solutions for a nonsymmetric
Keyfitz-Kranzer system with a Coulomb-like friction term or linear damping. We show the …

In this paper, we design and analyze a new class of positive Semi-Discrete Lagrangian–
Eulerian (SDLE) schemes for solving multidimensional initial value problems for scalar …

In this paper, we show how to construct a positive semi-discrete Lagrangian–Eulerian
scheme on triangular grids that asymptotically satisfies multidimensional scalar hyperbolic …

A new hyperbolic two-phase model of a porous deformable medium saturated with a viscous
fluid is presented and some of its features or performances are discussed. The governing …