Rekha Khot
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View article: Explicit Runge--Kutta schemes with hybrid high-order and weakGalerkin methods for the wave equation in first-order form
Explicit Runge--Kutta schemes with hybrid high-order and weakGalerkin methods for the wave equation in first-order form Open
We derive energy error estimates in a fully-discrete setting for the first-order wave equation in its Friedrichs formulation, using third- and fourth-order explicit Runge--Kutta (ERK3 and ERK4) schemes in time combined with hybrid high-ord…
View article: Hybrid high-order methods for elasto-acoustic wave propagation in the time domain
Hybrid high-order methods for elasto-acoustic wave propagation in the time domain Open
We devise a Hybrid High-Order (HHO) method for the coupling between the acoustic and elastic wave equations in the time domain. A first-order formulation in time is considered. The HHO method can use equal-order and mixed-order settings wi…
View article: A posteriori error analysis of a robust virtual element method for stress-assisted diffusion problems
A posteriori error analysis of a robust virtual element method for stress-assisted diffusion problems Open
We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between e…
View article: Explicit Runge-Kutta schemes with hybrid high-order methods for the wave equation in first-order form
Explicit Runge-Kutta schemes with hybrid high-order methods for the wave equation in first-order form Open
We analyze the approximation of the acoustic wave equation in its first-order Friedrichs formulation by explicit Runge-Kutta (ERK) schemes in time combined with hybrid high-order (HHO) methods in space. We propose two general assumptions (…
View article: Robust virtual element methods for coupled stress-assisted diffusion problems
Robust virtual element methods for coupled stress-assisted diffusion problems Open
This paper aims first to perform robust continuous analysis of a mixed nonlinear formulation for stress-assisted diffusion of a solute that interacts with an elastic material, and second to propose and analyse a virtual element formulation…
View article: Virtual element methods for Biot-Kirchhoff poroelasticity
Virtual element methods for Biot-Kirchhoff poroelasticity Open
This paper analyses conforming and nonconforming virtual element formulations of arbitrary polynomial degrees on general polygonal meshes for the coupling of solid and fluid phases in deformable porous plates. The governing equations consi…
View article: Conforming VEM for general second-order elliptic problems with rough data on polygonal meshes and its application to a Poisson inverse source problem
Conforming VEM for general second-order elliptic problems with rough data on polygonal meshes and its application to a Poisson inverse source problem Open
This paper focuses on the analysis of conforming virtual element methods for general second-order linear elliptic problems with rough source terms and applies it to a Poisson inverse source problem with rough measurements. For the forward …
View article: A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems
A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems Open
The nonconforming virtual element method (NCVEM) for the approximation of the weak solution to a general linear second-order non-selfadjoint indefinite elliptic PDE in a polygonal domain $$\Omega $$ is analyzed under reduced elliptic reg…
View article: Nonconforming virtual elements for the biharmonic equation with Morley degrees of freedom on polygonal meshes
Nonconforming virtual elements for the biharmonic equation with Morley degrees of freedom on polygonal meshes Open
The lowest-order nonconforming virtual element extends the Morley triangular element to polygons for the approximation of the weak solution $u\in V:=H^2_0(Ω)$ to the biharmonic equation. The abstract framework allows (even a mixture of) tw…
View article: A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems
A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems Open
The nonconforming virtual element method (NCVEM) for the approximation of the weak solution to a general linear second-order non-selfadjoint indefinite elliptic PDE in a polygonal domain is analyzed under reduced elliptic regularity. The m…