2019 
Droniou J, Ilyas M, Lamichhane BP, Wheeler GE, 'A mixed finite element method for a sixthorder elliptic problem', IMA Journal of Numerical Analysis, 39 374397 (2019)



2019 
Lamichhane BP, Lindstrom SB, Sims B, 'APPLICATION of PROJECTION ALGORITHMS to DIFFERENTIAL EQUATIONS: BOUNDARY VALUE PROBLEMS', ANZIAM Journal, (2019)
© 2019 Australian Mathematical Society. The DouglasRachford method has been employed successfully to solve many kinds of nonconvex feasibility problems. In particular, recent res... [more]
© 2019 Australian Mathematical Society. The DouglasRachford method has been employed successfully to solve many kinds of nonconvex feasibility problems. In particular, recent research has shown surprising stability for the method when it is applied to finding the intersections of hypersurfaces. Motivated by these discoveries, we reformulate a second order boundary value problem (BVP) as a feasibility problem where the sets are hypersurfaces. We show that such a problem may always be reformulated as a feasibility problem on no more than three sets and is well suited to parallelization. We explore the stability of the method by applying it to several BVPs, including cases where the traditional Newton's method fails.



2018 
Barnes MP, Menk FW, Lamichhane BP, Greer PB, 'A proposed method for linear accelerator photon beam steering using EPID', JOURNAL OF APPLIED CLINICAL MEDICAL PHYSICS, 19 591597 (2018) [C1]



2018 
Banz L, Lamichhane BP, Stephan EP, 'Higher order FEM for the obstacle problem of the pLaplacian¿A variational inequality approach', Computers and Mathematics with Applications, 76 16391660 (2018) [C1]



2018 
Banz L, Lamichhane BP, Stephan EP, 'Higher Order Mixed FEM for the Obstacle Problem of the pLaplace Equation Using Biorthogonal Systems', Computational Methods in Applied Mathematics, (2018)
© 2018 Walter de Gruyter GmbH, Berlin/Boston 2018 pLaplace Obstacle Problem. We consider a mixed finite element method for an obstacle problem with the pLaplace differential ope... [more]
© 2018 Walter de Gruyter GmbH, Berlin/Boston 2018 pLaplace Obstacle Problem. We consider a mixed finite element method for an obstacle problem with the pLaplace differential operator for p ¿ (1 ,8), where the obstacle condition is imposed by using a Lagrange multiplier. In the discrete setting the Lagrange multiplier basis forms a biorthogonal system with the standard finite element basis so that the variational inequality can be realized in the pointwise form. We provide a general a posteriori error estimate for adaptivity and prove an a priori error estimate. We present numerical results for the adaptive scheme (meshsize adaptivity with and without polynomial degree adaptation) for the singular case p = 1.5 {p=1.5} and the degenerated case p = 3 {p=3} . We also present numerical results on the mesh independency and on the polynomial degree scaling of the discrete infsup constant when using biorthogonal basis functions for the dual variable defined on the same mesh with the same polynomial degree distribution.



2018 
Ilyas M, Meylan MH, Lamichhane B, Bennetts LG, 'Timedomain and modal response of ice shelves to wave forcing using the finite element method', Journal of Fluids and Structures, 80 113131 (2018) [C1]
© 2018 Elsevier Ltd The frequencydomain and timedomain response of a floating ice shelf to wave forcing are calculated using the finite element method. The boundary conditions a... [more]
© 2018 Elsevier Ltd The frequencydomain and timedomain response of a floating ice shelf to wave forcing are calculated using the finite element method. The boundary conditions at the front of the ice shelf, coupling it to the surrounding fluid, are written as a special nonlocal linear operator with forcing. This operator allows the computational domain to be restricted to the water cavity beneath the ice shelf. The ice shelf motion is expanded using the in vacuo elastic modes and the method of added mass and damping, commonly used in the hydroelasticity of ships, is employed. The ice shelf is assumed to be of constant thickness while the fluid domain is allowed to vary. The analysis is extended from the frequency domain to the time domain, and the resonant behaviour of the system is studied. It is shown that shelf submergence affects the resonant vibration frequency, whereas the corresponding mode shapes are insensitive to the submergence in constant depth. Further, the modes are shown to have a property of increasing node number with increasing frequency.



2018 
Droniou J, Lamichhane BP, Shylaja D, 'The Hessian Discretisation Method for Fourth Order Linear Elliptic Equations', Journal of Scientific Computing, (2018)
© 2018, Springer Science+Business Media, LLC, part of Springer Nature. In this paper, we propose a unified framework, the Hessian discretisation method (HDM), which is based on fo... [more]
© 2018, Springer Science+Business Media, LLC, part of Springer Nature. 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 few intrinsic indicators of accuracy, independent of the considered model. An error estimate is obtained, using only these intrinsic indicators, when the HDM framework is applied to linear fourth order problems. It is shown that HDM encompasses a large number of numerical methods for fourth order elliptic problems: finite element methods (conforming and nonconforming) as well as finite volume methods. We also use the HDM to design a novel method, based on conforming P1 finite element space and gradient recovery operators. Results of numerical experiments are presented for this novel scheme and for a finite volume scheme.



2017 
Lamichhane BP, 'A NEW MINIMIZATION PRINCIPLE FOR THE POISSON EQUATION LEADING TO A FLEXIBLE FINITE ELEMENT APPROACH', ANZIAM JOURNAL, 59 232239 (2017) [C1]



2017 
Le KN, McLean W, Lamichhane B, 'FINITE ELEMENT APPROXIMATION of A TIMEFRACTIONAL DIFFUSION PROBLEM for A DOMAIN with A REENTRANT CORNER', ANZIAM Journal, 59 6182 (2017) [C1]
© 2017 Australian Mathematical Society. An initialboundary value problem for a timefractional diffusion equation is discretized in space, using continuous piecewiselinear finit... [more]
© 2017 Australian Mathematical Society. An initialboundary value problem for a timefractional diffusion equation is discretized in space, using continuous piecewiselinear finite elements on a domain with a reentrant corner. Known error bounds for the case of a convex domain break down, because the associated Poisson equation is no longer regular. In particular, the method is no longer secondorder accurate if quasiuniform triangulations are used. We prove that a suitable local mesh refinement about the reentrant corner restores secondorder convergence. In this way, we generalize known results for the classical heat equation.



2017 
Lamichhane BP, 'A quadrilateral 'mini' finite element for the stokes problem using a single bubble function', International Journal of Numerical Analysis and Modeling, 14 869878 (2017) [C1] 


2017 
Lamichhane BP, Gross L, 'Inversion of geophysical potential field data using the finite element method', INVERSE PROBLEMS, 33 (2017) [C1]



2017 
Banz L, Lamichhane BP, Stephan EP, 'A new threefield formulation of the biharmonic problem and its finite element discretization', NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 33 199217 (2017) [C1]



2016 
Lamichhane BP, Roberts SG, Stals L, 'A Mixed Finite Element Discretisation of Thin Plate Splines Based on Biorthogonal Systems', Journal of Scientific Computing, 67 2042 (2016) [C1]
© 2015, Springer Science+Business Media New York. The thin plate spline method is a widely used data fitting technique as it has the ability to smooth noisy data. Here we consider... [more]
© 2015, Springer Science+Business Media New York. The thin plate spline method is a widely used data fitting technique as it has the ability to smooth noisy data. Here we consider a mixed finite element discretisation of the thin plate spline. By using mixed finite elements the formulation can be defined interms of relatively simple stencils, thus resulting in a system that is sparse and whose size only depends linearly on the number of finite element nodes. The mixed formulation is obtained by introducing the gradient of the corresponding function as an additional unknown. The novel approach taken in this paper is to work with a pair of bases for the gradient and the Lagrange multiplier forming a biorthogonal system thus ensuring that the scheme is numerically efficient, and the formulation is stable. Some numerical results are presented to demonstrate the performance of our approach. A preconditioned conjugate gradient method is an efficient solver for the arising linear system of equations.



2015 
Lamichhane BP, 'A quadrilateral 'mini' finite element for the Stokes problem using a single bubble function.', CoRR, abs/1507.04417 (2015) [O1] 


2015 
Lamichhane BP, 'A new stabilization technique for the nonconforming CrouzeixRaviart element applied to linear elasticity', APPLIED MATHEMATICS LETTERS, 39 3541 (2015) [C1]



2015 
Droniou J, Lamichhane BP, 'Gradient schemes for linear and nonlinear elasticity equations', NUMERISCHE MATHEMATIK, 129 251277 (2015) [C1]



2015 
Lamichhane BP, McNeilly A, 'Approximation Properties of a Gradient Recovery Operator Using a Biorthogonal System', Advances in Numerical Analysis, 2015 17 (2015) [C1]



2014 
Lamichhane BP, 'A finite element method for a biharmonic equation based on gradient recovery operators', BIT NUMERICAL MATHEMATICS, 54 469484 (2014) [C1]



2014 
Lamichhane BP, 'A stabilized mixed finite element method based on gbiorthogonal systems for nearly incompressible elasticity', COMPUTERS & STRUCTURES, 140 4854 (2014) [C1]



2014 
Lamichhane BP, 'A nonconforming finite element method for the Stokes equations using the CrouzeixRaviart element for the velocity and the standard linear element for the pressure', INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 74 222228 (2014) [C1]



2014 
Lamichhane BP, Roberts SG, Hegland M, 'A new multivariate spline based on mixed partial derivatives and its finite element approximation', APPLIED MATHEMATICS LETTERS, 35 8285 (2014) [C1]



2014 
Lamichhane BP, 'A mixed finite element method for nearly incompressible elasticity and Stokes equations using primal and dual meshes with quadrilateral and hexahedral grids', Journal of Computational and Applied Mathematics, 260 356363 (2014) [C1]
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 quadrilate... [more]
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 quadrilateral and hexahedral triangulation using primal and dual meshes. We use the standard bilinear and trilinear finite element space enriched with elementwise defined bubble functions with respect to the primal mesh for the displacement or velocity, whereas the pressure space is discretized by using a piecewise constant finite element space with respect to the dual mesh. © 2013 Elsevier B.V. All rights reserved.



2013 
Lamichhane BP, 'A New Finite Element Method for DarcyStokesBrinkman Equations', ISRN Computational Mathematics, 2013 14 (2013) [C1] 


2013 
Lamichhane BP, 'Two simple finite element methods for ReissnerMindlin plates with clamped boundary condition', Applied Numerical Mathematics, 72 9198 (2013) [C1]
We present two simple finite element methods for the discretization of ReissnerMindlin plate equations with clamped boundary condition. These finite element methods are based on ... [more]
We present two simple finite element methods for the discretization of ReissnerMindlin plate equations with clamped boundary condition. These finite element methods are based on discrete Lagrange multiplier spaces from mortar finite element techniques. We prove optimal a priori error estimates for both methods. The first approach is based on a socalled standard Lagrange multiplier space for the mortar finite element method, where the Lagrange multiplier basis functions are continuous. The second approach is based on a socalled dual Lagrange multiplier space, where the Lagrange multiplier basis functions are discontinuous. The advantage of using the second approach is that easy static condensation of degrees of freedom corresponding to the Lagrange multiplier is possibly leading to a symmetric positive definite formulation. © 2013 IMACS. Published by Elsevier B.V. All rights reserved.



2013 
Lamichhane BP, McBride AT, Reddy BD, 'A finite element method for a threefield formulation of linear elasticity based on biorthogonal systems', Computer Methods in Applied Mechanics and Engineering, 258 109117 (2013) [C1]
We consider a mixed finite element method based on simplicial triangulations for a threefield formulation of linear elasticity. The threefield formulation is based on three unkn... [more]
We consider a mixed finite element method based on simplicial triangulations for a threefield formulation of linear elasticity. The threefield formulation is based on three unknowns: displacement, stress and strain. In order to obtain an efficient discretization scheme, we use a pair of finite element bases forming a biorthogonal system for the strain and stress. The biorthogonality relation allows us to statically condense out the strain and stress from the saddlepoint system leading to a symmetric and positivedefinite system. The strain and stress can be recovered in a postprocessing step simply by inverting a diagonal matrix. Moreover, we show a uniform convergence of the finite element approximation in the incompressible limit. Numerical experiments are presented to support the theoretical results. © 2013 Elsevier B.V.



2013 
Lamichhane BP, 'Mixed Finite Element Methods for the Poisson Equation Using Biorthogonal and QuasiBiorthogonal Systems', Advances in Numerical Analysis, 2013 19 (2013) [C1]



2011 
Lamichhane BP, 'A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems', Journal of Computational and Applied Mathematics, 235 51885197 (2011) [C1]



2011 
Lamichhane BP, Stephan EP, 'A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems', Numerical Methods for Partial Differential Equations, 28 13361353 (2011) [C1]



2011 
Lamichhane BP, 'A mixed finite element method for the biharmonic problem using biorthogonal or quasibiorthogonal systems', Journal of Scientific Computing, 46 379396 (2011) [C1]



2010 
Lamichhane BP, 'A gradient recovery operator based on an oblique projection', Electronic Transactions on Numerical Analysis, 37 166172 (2010) [C1]



2009 
Lamichhane BP, 'Mortar finite elements for coupling compressible and nearly incompressible materials in elasticity', INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 6 177192 (2009) [C1]



2009 
Falletta S, Lamichhane BP, 'Mortar finite elements for a heat transfer problem on sliding meshes', CALCOLO, 46 131148 (2009) [C1]



2009 
Lamichhane BP, 'A mixed finite element method for nonlinear and nearly incompressible elasticity based on biorthogonal systems', INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 79 870886 (2009) [C1]



2009 
Lamichhane BP, 'From the HuWashizu formulation to the average nodal strain formulation', COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 198 39573961 (2009) [C1]



2009 
Lamichhane BP, 'Infsup stable finiteelement pairs based on dual meshes and bases for nearly incompressible elasticity', IMA JOURNAL OF NUMERICAL ANALYSIS, 29 404420 (2009) [C1]



2009 
Lamichhane BP, 'Finite Element Techniques for Removing the Mixture of Gaussian and Impulsive Noise', IEEE TRANSACTIONS ON SIGNAL PROCESSING, 57 25382547 (2009) [C2]



2008 
Lamichhane BP, 'A mixed finite element method based on a biorthogonal system for nearly incompressible elastic problems', ANZIAM Journal, 50 324338 (2008) [C1]



2007 
Chavan KS, Lantichhane BP, Wohmuth BI, 'Lockingfree finite element methods for linear and nonlinear elasticity in 2D and 3D', COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 196 40754086 (2007)



2007 
Chavan KS, Lamichhane BP, Wohlmuth BI, 'Lockingfree finite element methods for linear and nonlinear elasticity in 2D and 3D', Computer Methods in Applied Mechanics and Engineering, 196 40754086 (2007)
The uniform convergence of finite element approximations based on a modified HuWashizu formulation for the nearly incompressible linear elasticity is analyzed. We show the optima... [more]
The uniform convergence of finite element approximations based on a modified HuWashizu formulation for the nearly incompressible linear elasticity is analyzed. We show the optimal and robust convergence of the displacementbased discrete formulation in the nearly incompressible case with the choice of approximations based on quadrilateral and hexahedral elements. These choices include bases that are well known, as well as newly constructed bases. Starting from a suitable threefield problem, we extend our adependent threefield formulation to geometrically nonlinear elasticity with SaintVenant Kirchhoff law. Additionally, an adependent threefield formulation for a general hyperelastic material model is proposed. A range of numerical examples using different material laws for small and large strain elasticity is presented. © 2007 Elsevier B.V. All rights reserved.



2006 
Lamichhane BP, Wohlmuth BI, 'Biorthogonal bases with local support and approximation properties', MATHEMATICS OF COMPUTATION, 76 233249 (2006)



2006 
Lamichhane BP, Reddy BD, Wohlmuth BI, 'Convergence in the incompressible limit of finite element approximations based on the HuWashizu formulation', NUMERISCHE MATHEMATIK, 104 151175 (2006)



2006 
Djoko JK, Lamichhane BP, Reddy BD, Wohmuth BI, 'Conditions for equivalence between the HuWashizu and related formulations, and computational behavior in the incompressible limit', COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 195 41614178 (2006)



2005 
Lamichhane BP, Stevenson RP, Wohlmuth BI, 'Higher order mortar finite element methods in 3D with dual lagrange multiplier bases', NUMERISCHE MATHEMATIK, 102 93121 (2005)



2004 
Lamichhane BP, Wohlmuth BI, 'Mortar finite elements for interface problems', COMPUTING, 72 333348 (2004)



2004 
Lamichhane BP, Wohlmuth BI, 'A quasidual Lagrange multiplier space for serendipity mortar finite elements in 3D', ESAIMMATHEMATICAL MODELLING AND NUMERICAL ANALYSISMODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 38 7392 (2004)



2002 
Lamichhane BP, Wohlmuth BI, 'Higher order dual Lagrange multiplier spaces for mortar finite element discretizations', CALCOLO, 39 219237 (2002)


