|2015||Lamichhane BP, 'A new stabilization technique for the nonconforming Crouzeix-Raviart element applied to linear elasticity', APPLIED MATHEMATICS LETTERS, 39 35-41 (2015) [C1]|
|2015||Lamichhane BP, 'A new stabilization technique for the nonconforming Crouzeix-Raviart element applied to linear elasticity', Applied Mathematics Letters, 39 35-41 (2015) [C1]|
|2014||Lamichhane BP, 'A finite element method for a biharmonic equation based on gradient recovery operators', BIT NUMERICAL MATHEMATICS, 54 469-484 (2014) [C1]|
|2014||Droniou J, Lamichhane BP, 'Gradient schemes for linear and non-linear elasticity equations', Numerische Mathematik, (2014)|
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 scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numerical methods for elasticity are embedded in the gradient scheme framework, which allows us to obtain convergence results for these methods in cases where the solution does not satisfy the full (Formula presented.)-regularity or for non-linear models. Â© 2014 Springer-Verlag Berlin Heidelberg.
|2014||Lamichhane BP, 'A stabilized mixed finite element method based on g-biorthogonal systems for nearly incompressible elasticity', COMPUTERS & STRUCTURES, 140 48-54 (2014) [C1]|
|2014||Lamichhane BP, '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', INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 74 222-228 (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, 260 356-363 (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 quadrilateral and hexahedral triangulation using primal and dual meshes. We use the standard bilinear and trilinear finite element space enriched with element-wise 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. Â© 2013 Elsevier B.V. All rights reserved.
|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 82-85 (2014) [C1]|
|2013||Lamichhane BP, 'A New Finite Element Method for Darcy-Stokes-Brinkman Equations', ISRN Computational Mathematics, 2013 1-4 (2013) [C1]|
|2013||Lamichhane BP, McBride AT, Reddy BD, 'A finite element method for a three-field formulation of linear elasticity Cross Mark based on biorthogonal systems', COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 258 109-117 (2013) [C1]|
|2013||Lamichhane BP, 'Two simple finite element methods for Reissner-Mindlin plates with clamped boundary condition', Applied Numerical Mathematics, 72 91-98 (2013) [C1]|
We present two simple finite element methods for the discretization of Reissner-Mindlin 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 so-called 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 so-called 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. Â© 2013 IMACS. Published by Elsevier B.V. All rights reserved.
|2013||Lamichhane BP, 'Mixed Finite Element Methods for the Poisson Equation Using Biorthogonal and Quasi-Biorthogonal Systems', Advances in Numerical Analysis, 2013 1-9 (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 5188-5197 (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 1336-1353 (2011) [C1]|| |
|2011||Lamichhane BP, 'A mixed finite element method for the biharmonic problem using biorthogonal or quasi-biorthogonal systems', Journal of Scientific Computing, 46 379-396 (2011) [C1]|| |
|2010||Lamichhane BP, 'A gradient recovery operator based on an oblique projection', Electronic Transactions on Numerical Analysis, 37 166-172 (2010) [C1]|| |
|2007||Chavan KS, Lamichhane BP, Wohlmuth BI, 'Locking-free finite element methods for linear and nonlinear elasticity in 2D and 3D', Computer Methods in Applied Mechanics and Engineering, 196 4075-4086 (2007)|
The uniform convergence of finite element approximations based on a modified Hu-Washizu formulation for the nearly incompressible linear elasticity is analyzed. We show the optimal and robust convergence of the displacement-based 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 three-field problem, we extend our a-dependent three-field formulation to geometrically nonlinear elasticity with Saint-Venant Kirchhoff law. Additionally, an a-dependent three-field 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. Â© 2007 Elsevier B.V. All rights reserved.
|2006||Lamichhane BP, Wohlmuth BI, 'Biorthogonal bases with local support and approximation properties', MATHEMATICS OF COMPUTATION, 76 233-249 (2006)|
|2006||Lamichhane BP, Reddy BD, Wohlmuth BI, 'Convergence in the incompressible limit of finite element approximations based on the Hu-Washizu formulation', NUMERISCHE MATHEMATIK, 104 151-175 (2006)|
|2006||Djoko JK, Lamichhane BP, Reddy BD, Wohmuth BI, 'Conditions for equivalence between the Hu-Washizu and related formulations, and computational behavior in the incompressible limit', COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 195 4161-4178 (2006)|
|2005||Lamichhane BP, Wohlmuth BI, 'Mortar finite elements with dual Lagrange multipliers: Some applications', DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING, 40 319-326 (2005)|
|2005||Lamichhane BP, Stevenson RP, Wohlmuth BI, 'Higher order mortar finite element methods in 3D with dual lagrange multiplier bases', NUMERISCHE MATHEMATIK, 102 93-121 (2005)|
|2004||Lamichhane BP, Wohlmuth BI, 'Mortar finite elements for interface problems', COMPUTING, 72 333-348 (2004)|
|2004||Lamichhane BP, Wohlmuth BI, 'A quasi-dual Lagrange multiplier space for serendipity mortar finite elements in 3D', ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 38 73-92 (2004)|
|2002||Lamichhane BP, Wohlmuth BI, 'Higher order dual Lagrange multiplier spaces for mortar finite element discretizations', CALCOLO, 39 219-237 (2002)|