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In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the underlying problem. Unconditional L2-stability and error estimate of order O τr+1+ hk+1/2 are obtained when polynomials of degree at most r and k are used for the temporal discretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r + 1 in temporal variable t. 相似文献
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L^2-ERROR OF EXTRAPOLATION CASCADIC MULTIGRID (EXCMG) 总被引:1,自引:0,他引:1
Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method (EXCMG) is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG. 相似文献
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This article will combine the finite element method, the interpolated coefftcient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilinear elliptic equations. This strategy not only grently reduces the expensive computation, but also is successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems with non-odd nonlinearity on some convex or nonconvex domains. Numerical solutions illustrated by their graphics for visualization will show the efficiency of the approach. 相似文献
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谢资清 《数学物理学报(B辑英文版)》1998,(2)
1IntroductionLetnbeaboundeddomaininRewithCIboundarytn23.Weconsidertheprobleminwhichp=ac,q=M,7denotestheunitoutwardnormaltoon,A>0,p20.Inthisp8Per,wesuppose(Al)a(z)eL"(n),a(z)50.(afl)op(2)EC(on),op(x)20,M==op(:).(op2)op(zo)=M,icEOf.InasmallneighborhoodUofic,thedoesnQliesononesideOfthetangentplaneOfonatic,andthe(n--l)principlecurvaturesofxo(withrespecttotheinnernormalOfon)arepositive.(gi)g(z,u)ismeasurablein2,continuousinu,sup{g(2,u)::En,0Su5an}< coforeveryfixedan>0andg(x,0)=0.(g2)!5op=0… 相似文献
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1 IntroductionWe deal with the problem{ it:;,."--'"'::3of (11)where 9 C RN, N 2 3 is a bounded domain with smooth boundary 0fl, 0n = ro U r1, ro andYl have (N -- 1)-dinlensiollal Hausdorff nleasuret r E L'(r1), yt 2 0, V * 0 on r1, 7 denotesthe u11it outward normal and p = 2* = ee is the critical SoboleY exponent fOr the Sobolevembedding V(O) - H(O), V(fl) = {u E H'(fl) l u = 0 on ro}'The case ro and r1 have positive (N -- 1)-dimellsional Hausdoor measure aud p = 0on r1 in (1.1), has… 相似文献
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In this article, we introduce a coupled approach of local discontinuous Galerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. The discontinuous Galerkin method is adopted in the subdomain where the solution varies rapidly, while the standard finite element method is used in the other subdomain due to its lower computational cost. The stability and a priori error estimate are established. We prove that the coupled method has O((ε1 / 2 + h 1 / 2 )h k ) convergence rate in an associated norm, where ε is the diffusion coefficient, h is the mesh size and k is the degree of polynomial. The numerical results verify our theoretical results. Moreover, 2k-order superconvergence of the numerical traces at the nodes, and the optimal convergence of the errors under L 2 norm are observed numerically on the uniform mesh. The numerical results also indicate that the coupled method has the same convergence order and almost the same errors as the purely LDG method. 相似文献
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In this paper, we propose an accelerated search-extension method (ASEM) based on the interpolated coefficient finite element method, the search-extension method (SEM) and the two-grid method to obtain the multiple solutions for semilinear elliptic equations. This strategy is not only successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems, but also reduces the expensive computation greatly. The numerical results in I-D and 2-D cases will show the efficiency of our approach. 相似文献