19 citations · 42 across the 20 of their papers we have counts for
24 papers
An ultra-weak three-field finite element formulation for the biharmonic and extended Fisher--Kolmogorov equations
Rekha Khot, Bishnu P. Lamichhane, Ricardo Ruiz-Baier
This paper discusses a so-called ultra-weak three-field formulation of the biharmonic problem where the solution, its gradient, and an additional Lagrange multiplier are the three…
Efficient Data-Driven Leverage Score Sampling Algorithm for the Minimum Volume Covering Ellipsoid Problem in Big Data
Elizabeth Harris, Ali Eshragh, Bishnu Lamichhane +2
The Minimum Volume Covering Ellipsoid (MVCE) problem, characterised by observations in dimensions where , can be computationally very expensive in the big data reg…
A priori and a posteriori error bounds for the fully mixed FEM formulation of poroelasticity with stress-dependent permeability
Arbaz Khan, Bishnu P. Lamichhane, Ricardo Ruiz-Baier +1
We develop a family of mixed finite element methods for a model of nonlinear poroelasticity where, thanks to a rewriting of the constitutive equations, the permeability depends on…
New twofold saddle-point formulations for Biot poroelasticity with porosity-dependent permeability
Bishnu P. Lamichhane, Ricardo Ruiz-Baier, Segundo Villa-Fuentes
We propose four-field and five-field Hu--Washizu-type mixed formulations for nonlinear poroelasticity -- a coupled fluid diffusion and solid deformation process -- considering that…
On q-statistical approximation of wavelets aided Kantorovich q-Baskakov operators
Mohammad Ayman-Mursaleen, Bishnu P. Lamichhane, Adem Kiliçman +1
The aim of this research is to examine various statistical approximation properties with respect to Kantorovich \textit{\text{\texthtq}}-Baskakov operators using wavelets. We discu…
An optimal error estimate for a mixed finite element method for a biharmonic problem with clamped boundary conditions
Bishnu P Lamichhane
We consider a mixed finite element method for a biharmonic equation with clamped boundary conditions based on biorthogonal systems with weakly imposed Dirichlet boundary condition.…
Swell induced vibrations of a thickening ice shelf over a shoaling seabed
Michael Meylan, Muhammad Ilyas, Bishnu Lamichhane +1
A solution method is developed for a model of ice shelf vibrations in response to ocean waves, in which the ice shelf thickness and seabed beneath the ice shelf vary over distance,…
Approximation of noisy data using multivariate splines and finite element methods
Elizabeth Harris, Bishnu Lamichhane, Quoc Thong Le Gia
We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defi…
Energy Resolved Neutron Imaging for Strain Reconstruction using the Finite Element Method
Riya Aggarwal, Mike Meylan, Bishnu Lamichhane +1
A pulsed neutron imaging technique is used to reconstruct the residual strain within a polycrystalline material from Bragg edge strain images. This technique offers the possibility…
The Hessian discretisation method for fourth order linear elliptic equations
Jérôme Droniou, Bishnu P. Lamichhane, Devika Shylaja
In this paper, we propose a unified framework, the Hessian discretisation method (HDM), which is based on four discrete elements (called altogether a Hessian discretisation) and a…
A three-field formulation of the Poisson problem with Nitsche approach
Muhammad Ilyas, Bishnu P. Lamichhane
We modify a three-field formulation of the Poisson problem with Nitsche approach for approximating Dirichlet boundary conditions. Nitsche approach allows us to weakly impose Dirich…
A mixed finite element method for a sixth order elliptic problem
Jérôme Droniou, Muhammad Ilyas, Bishnu Lamichhane +1
We consider a saddle point formulation for a sixth order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciar…
Application of projection algorithms to differential equations: boundary value problems
Bishnu P. Lamichhane, Scott B. Lindstrom, Brailey Sims
The Douglas-Rachford method has been employed successfully to solve many kinds of non-convex feasibility problems. In particular, recent research has shown surprising stability for…
Finite element approximation of a time-fractional diffusion problem in a non-convex polygonal domain
Kim Ngan Le, William McLean, Bishnu Lamichhane
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a…
A New Minimisation Principle for Poisson Equation Leading to a Flexible Finite Element Approach
Bishnu P. Lamichhane
We introduce a new minimisation principle for Poisson equation using two variables: the solution and the gradient of the solution. This principle allows us to use any conforming fi…
A quadrilateral 'mini' finite element for the Stokes problem using a single bubble function
Bishnu P. Lamichhane
We consider a quadrilateral 'mini' finite element for approximating the solution of Stokes equations using a quadrilateral mesh. We use the standard bilinear finite element space e…
Gradient Schemes for Linear and Non-linear Elasticity Equations
Jerome Droniou, Bishnu P. Lamichhane
The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient…
A simple finite element method for Reissner--Mindlin plate equations using the Crouzeix-Raviart element and the standard linear finite element
Bishnu P Lamichhane
We present a simple finite element method for the discretization of Reissner--Mindlin plate equations. The finite element method is based on using the nonconforming Crouzeix-Raviar…
A nonconforming finite element method for the Stokes equations using the Crouzeix-Raviart element for the velocity and the standard linear element for the pressure
Bishnu P. Lamichhane
We present a finite element method for Stokes equations using the Crouzeix-Raviart element for the velocity and the continuous linear element for the pressure. We show that the inf…
A mixed finite element method for nearly incompressible elasticity and Stokes equations using primal and dual meshes with quadrilateral and hexahedral grids
Bishnu P. Lamichhane
We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilater…
Two simple finite element methods for Reissner--Mindlin plates with clamped boundary condition
Bishnu P. Lamichhane
We present two simple finite element methods for the discretization of Reissner--Mindlin plate equations with {\em clamped} boundary condition. These finite element methods are bas…
Approximation Properties of a Gradient Recovery Operator Using a Biorthogonal System
Bishnu P. Lamichhane, Adam McNeily
A gradient recovery operator based on projecting the discrete gradient onto the standard finite element space is considered. We use an oblique projection, where the test and trial…
A Stabilized Mixed Finite Element Method for Thin Plate Splines Based on Biorthogonal Systems
Bishnu P. Lamichhane, Markus Hegland
The thin plate spline is a popular tool for the interpolation and smoothing of scattered data. In this paper we propose a novel stabilized mixed finite element method for the discr…
Sparse Representations for Structured Noise Filtering
Bishnu P. Lamichhane, Laura Rebollo-Neira
The role of sparse representations in the context of structured noise filtering is discussed. A strategy, especially conceived so as to address problems of an ill posed nature, is…